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Show that there exists an integer that is a power of 5 with the first 4 digits being 2018.
Given $2^x=129$, why is it that I can use the natural logarithm to find $x$?Satisfying equality between logarithmic expressionsDividing logarithms without using a calculatorIf $a=blog b$, how does $b$ grow asymptotically?So many logs with different basesComparing functions that have logs in exponentsHow to show that $- log_b x = log_frac1b x$Taking log of a matrix equationhow to simplify a quadratic logarithmic equation equation?
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
I know the problem can be expressed in the following way. Let $a,b in mathbbZ^+$ such that $2018:times:10^b < 5^a < 2019:times:10^b$
Taking logs, I get $b + log 2018 < a log 5< b + log 2019$.
Not quite sure how else to proceed though.
logarithms
asked 10 hours ago
Haikal YeoHaikal Yeo
1,0638 silver badges23 bronze badges
$endgroup$
add a comment |
$begingroup$
I know the problem can be expressed in the following way. Let $a,b in mathbbZ^+$ such that $2018:times:10^b < 5^a < 2019:times:10^b$
Taking logs, I get $b + log 2018 < a log 5< b + log 2019$.
Not quite sure how else to proceed though.
logarithms
asked 10 hours ago
Haikal YeoHaikal Yeo
1,0638 silver badges23 bronze badges
$endgroup$
$begingroup$
Note: $5^92=2019....$
$endgroup$
– J. W. Tanner
10 hours ago
5
$begingroup$
$5^4364=2.018826153906575ldotscdot 10^3050$.
$endgroup$
– Christian Blatter
10 hours ago
add a comment |
$begingroup$
I know the problem can be expressed in the following way. Let $a,b in mathbbZ^+$ such that $2018:times:10^b < 5^a < 2019:times:10^b$
Taking logs, I get $b + log 2018 < a log 5< b + log 2019$.
Not quite sure how else to proceed though.
logarithms
asked 10 hours ago
Haikal YeoHaikal Yeo
1,0638 silver badges23 bronze badges
$endgroup$
I know the problem can be expressed in the following way. Let $a,b in mathbbZ^+$ such that $2018:times:10^b < 5^a < 2019:times:10^b$
Taking logs, I get $b + log 2018 < a log 5< b + log 2019$.
Not quite sure how else to proceed though.
logarithms
logarithms
asked 10 hours ago
Haikal YeoHaikal Yeo
1,0638 silver badges23 bronze badges
asked 10 hours ago
Haikal YeoHaikal Yeo
1,0638 silver badges23 bronze badges
asked 10 hours ago
Haikal YeoHaikal Yeo
1,0638 silver badges23 bronze badges
asked 10 hours ago
Haikal YeoHaikal Yeo
1,0638 silver badges23 bronze badges
asked 10 hours ago
Haikal YeoHaikal Yeo
1,0638 silver badges23 bronze badges
1,0638 silver badges23 bronze badges
$begingroup$
Note: $5^92=2019....$
$endgroup$
– J. W. Tanner
10 hours ago
5
$begingroup$
$5^4364=2.018826153906575ldotscdot 10^3050$.
$endgroup$
– Christian Blatter
10 hours ago
add a comment |
$begingroup$
Note: $5^92=2019....$
$endgroup$
– J. W. Tanner
10 hours ago
5
$begingroup$
$5^4364=2.018826153906575ldotscdot 10^3050$.
$endgroup$
– Christian Blatter
10 hours ago
$begingroup$
Note: $5^92=2019....$
$endgroup$
– J. W. Tanner
10 hours ago
$begingroup$
Note: $5^92=2019....$
$endgroup$
– J. W. Tanner
10 hours ago
5
5
$begingroup$
$5^4364=2.018826153906575ldotscdot 10^3050$.
$endgroup$
– Christian Blatter
10 hours ago
$begingroup$
$5^4364=2.018826153906575ldotscdot 10^3050$.
$endgroup$
– Christian Blatter
10 hours ago
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
The set $A = a log_10 5 + b : a,b in mathbb Z $ is an additive subgroup of $mathbb R$, and so is either cyclic or dense.
If $A$ were cyclic, then $1 = n (a_0 log_10 5 + b_0)$. Since $log_10 5$ is irrational, we must have $n a_0 =0$ and $n b_0 = 1$, which cannot happen.
Therefore, $A$ is dense and so there is an element of $A$ in the interval $(log_10(2018), log_10(2019))$.
answered 9 hours ago
lhflhf
174k12 gold badges179 silver badges418 bronze badges
$endgroup$
$begingroup$
But what if $a <0$? ;)
$endgroup$
– N. S.
20 mins ago
add a comment |
$begingroup$
Hint Since $log_10(5)$ is irrational, the set $ a log_10(5)-b : a, b in mathbb N$ is dense in $mathbb R$. Therefore, you can find such a number in the interval $(log_10(2018), log_10(2019))$.
answered 10 hours ago
N. S.N. S.
109k7 gold badges118 silver badges215 bronze badges
$endgroup$
add a comment |
$begingroup$
201882615390657491958528733888359303897206738410754045263963565695705442119457224168899440239407953138581226299365782567442925725493850667127823188129261463991440173793523996779651936654389368686597194439736208695989862156299629602332523464076512669290731774513558552819180354651303963581641490360308535552425419867299337653389070510045424468908107895566363643482640162372352948553283421340038905458554369108404396575106064121414101960663718546239386527523409161552124792218268239338974867937280489575854266372435173446464066145926791484234116593481699639727998774125414871721332982942016722814109084246332819815465119939678154783718052333181096038896636579784807212135999682794464880561777058643610122484366550692964046735317370672168782581592297953410438100999375161197662519910850059633016528523568042285302742062098814548246723733888013653327016324124727737686998618632277442820374655493093729902407403246796933589232379520684294387357381354286158732655143619009740514672918111683766211391182403531198532559980151972513489907217185072196731637657634674068559899298805500983571984624086190968818017889989749154302003358764408667797989976730972834651878998380425225936897264605310688663029535576600866502864768965770091351971521995641025227860905919121596849003861094298243892705486363508792818416683489930886591576035182909921868555205172091169698191585767546957494046847024226730833257159854651007706945782566951387958682409697454133730086314492661919431019883237423708525758459729006177183221902634043244036721957840616924771617991861189108596959612503053521704057188513232970211432467080796220044513875134615739794385874670476886205780889353138817697126168129565683692421875294802472389184825853664308097076451463513926649779788130377406299829608329206810680213500593258029567966685039842829425254271550324266936497912430799186821435764991658842175752107255972699604608610838678647922991780897811201255157892448118302260686546980422098465087256649477365011881596878199059608414801013417027677837816041537974933022551966344978889501537172467203506670958637174099226979184380737481324329743693108262765896755437598412730342468865474573477004619362456714144985785078817902129543526158982694832379771931581941839225962375548217493133113050127913932315166413560509241349541568784192095222792848694381349868462030138524690958834727087880318746593234222439280165442150519813234371751409660250721132893912068388675454902832327537395026029852373100586738988362442544910516664069691179659777362156805235491174484504759330371215949360906031780262687660002512614551478392076625118081138080259140457229066530352113989013066692570397437773702413957231955020804389634415750498870634142816046788045672568297485242527508630207469164390742003932759774267358556602879306918807555750836800249985550904087271797537215843856934114642382854402532562504961847107385321625601211533133161511192639301728105746220687191517987404378034935607228167440448968116089808516638097060020070846318846918229693351291405338045145821917930096557614039198824684717692434787750244140625 = 5 ^ 4346
answered 49 mins ago
andrew.punnettandrew.punnett
933 bronze badges
New contributor
andrew.punnett is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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2
$begingroup$
While an exact answer does answer the question, exactly how you worked that out would probably be more useful to the person asking the question.
$endgroup$
– Ispil
38 mins ago
add a comment |
Your Answer
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3 Answers
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active
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3 Answers
3
active
oldest
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active
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$begingroup$
The set $A = a log_10 5 + b : a,b in mathbb Z $ is an additive subgroup of $mathbb R$, and so is either cyclic or dense.
If $A$ were cyclic, then $1 = n (a_0 log_10 5 + b_0)$. Since $log_10 5$ is irrational, we must have $n a_0 =0$ and $n b_0 = 1$, which cannot happen.
Therefore, $A$ is dense and so there is an element of $A$ in the interval $(log_10(2018), log_10(2019))$.
answered 9 hours ago
lhflhf
174k12 gold badges179 silver badges418 bronze badges
$endgroup$
$begingroup$
But what if $a <0$? ;)
$endgroup$
– N. S.
20 mins ago
add a comment |
$begingroup$
The set $A = a log_10 5 + b : a,b in mathbb Z $ is an additive subgroup of $mathbb R$, and so is either cyclic or dense.
If $A$ were cyclic, then $1 = n (a_0 log_10 5 + b_0)$. Since $log_10 5$ is irrational, we must have $n a_0 =0$ and $n b_0 = 1$, which cannot happen.
Therefore, $A$ is dense and so there is an element of $A$ in the interval $(log_10(2018), log_10(2019))$.
answered 9 hours ago
lhflhf
174k12 gold badges179 silver badges418 bronze badges
$endgroup$
$begingroup$
But what if $a <0$? ;)
$endgroup$
– N. S.
20 mins ago
add a comment |
$begingroup$
The set $A = a log_10 5 + b : a,b in mathbb Z $ is an additive subgroup of $mathbb R$, and so is either cyclic or dense.
If $A$ were cyclic, then $1 = n (a_0 log_10 5 + b_0)$. Since $log_10 5$ is irrational, we must have $n a_0 =0$ and $n b_0 = 1$, which cannot happen.
Therefore, $A$ is dense and so there is an element of $A$ in the interval $(log_10(2018), log_10(2019))$.
answered 9 hours ago
lhflhf
174k12 gold badges179 silver badges418 bronze badges
$endgroup$
The set $A = a log_10 5 + b : a,b in mathbb Z $ is an additive subgroup of $mathbb R$, and so is either cyclic or dense.
If $A$ were cyclic, then $1 = n (a_0 log_10 5 + b_0)$. Since $log_10 5$ is irrational, we must have $n a_0 =0$ and $n b_0 = 1$, which cannot happen.
Therefore, $A$ is dense and so there is an element of $A$ in the interval $(log_10(2018), log_10(2019))$.
answered 9 hours ago
lhflhf
174k12 gold badges179 silver badges418 bronze badges
answered 9 hours ago
lhflhf
174k12 gold badges179 silver badges418 bronze badges
answered 9 hours ago
lhflhf
174k12 gold badges179 silver badges418 bronze badges
answered 9 hours ago
lhflhf
174k12 gold badges179 silver badges418 bronze badges
174k12 gold badges179 silver badges418 bronze badges
$begingroup$
But what if $a <0$? ;)
$endgroup$
– N. S.
20 mins ago
add a comment |
$begingroup$
But what if $a <0$? ;)
$endgroup$
– N. S.
20 mins ago
$begingroup$
But what if $a <0$? ;)
$endgroup$
– N. S.
20 mins ago
$begingroup$
But what if $a <0$? ;)
$endgroup$
– N. S.
20 mins ago
add a comment |
$begingroup$
Hint Since $log_10(5)$ is irrational, the set $ a log_10(5)-b : a, b in mathbb N$ is dense in $mathbb R$. Therefore, you can find such a number in the interval $(log_10(2018), log_10(2019))$.
answered 10 hours ago
N. S.N. S.
109k7 gold badges118 silver badges215 bronze badges
$endgroup$
add a comment |
$begingroup$
Hint Since $log_10(5)$ is irrational, the set $ a log_10(5)-b : a, b in mathbb N$ is dense in $mathbb R$. Therefore, you can find such a number in the interval $(log_10(2018), log_10(2019))$.
answered 10 hours ago
N. S.N. S.
109k7 gold badges118 silver badges215 bronze badges
$endgroup$
add a comment |
$begingroup$
Hint Since $log_10(5)$ is irrational, the set $ a log_10(5)-b : a, b in mathbb N$ is dense in $mathbb R$. Therefore, you can find such a number in the interval $(log_10(2018), log_10(2019))$.
answered 10 hours ago
N. S.N. S.
109k7 gold badges118 silver badges215 bronze badges
$endgroup$
Hint Since $log_10(5)$ is irrational, the set $ a log_10(5)-b : a, b in mathbb N$ is dense in $mathbb R$. Therefore, you can find such a number in the interval $(log_10(2018), log_10(2019))$.
answered 10 hours ago
N. S.N. S.
109k7 gold badges118 silver badges215 bronze badges
answered 10 hours ago
N. S.N. S.
109k7 gold badges118 silver badges215 bronze badges
answered 10 hours ago
N. S.N. S.
109k7 gold badges118 silver badges215 bronze badges
answered 10 hours ago
N. S.N. S.
109k7 gold badges118 silver badges215 bronze badges
109k7 gold badges118 silver badges215 bronze badges
add a comment |
add a comment |
$begingroup$
201882615390657491958528733888359303897206738410754045263963565695705442119457224168899440239407953138581226299365782567442925725493850667127823188129261463991440173793523996779651936654389368686597194439736208695989862156299629602332523464076512669290731774513558552819180354651303963581641490360308535552425419867299337653389070510045424468908107895566363643482640162372352948553283421340038905458554369108404396575106064121414101960663718546239386527523409161552124792218268239338974867937280489575854266372435173446464066145926791484234116593481699639727998774125414871721332982942016722814109084246332819815465119939678154783718052333181096038896636579784807212135999682794464880561777058643610122484366550692964046735317370672168782581592297953410438100999375161197662519910850059633016528523568042285302742062098814548246723733888013653327016324124727737686998618632277442820374655493093729902407403246796933589232379520684294387357381354286158732655143619009740514672918111683766211391182403531198532559980151972513489907217185072196731637657634674068559899298805500983571984624086190968818017889989749154302003358764408667797989976730972834651878998380425225936897264605310688663029535576600866502864768965770091351971521995641025227860905919121596849003861094298243892705486363508792818416683489930886591576035182909921868555205172091169698191585767546957494046847024226730833257159854651007706945782566951387958682409697454133730086314492661919431019883237423708525758459729006177183221902634043244036721957840616924771617991861189108596959612503053521704057188513232970211432467080796220044513875134615739794385874670476886205780889353138817697126168129565683692421875294802472389184825853664308097076451463513926649779788130377406299829608329206810680213500593258029567966685039842829425254271550324266936497912430799186821435764991658842175752107255972699604608610838678647922991780897811201255157892448118302260686546980422098465087256649477365011881596878199059608414801013417027677837816041537974933022551966344978889501537172467203506670958637174099226979184380737481324329743693108262765896755437598412730342468865474573477004619362456714144985785078817902129543526158982694832379771931581941839225962375548217493133113050127913932315166413560509241349541568784192095222792848694381349868462030138524690958834727087880318746593234222439280165442150519813234371751409660250721132893912068388675454902832327537395026029852373100586738988362442544910516664069691179659777362156805235491174484504759330371215949360906031780262687660002512614551478392076625118081138080259140457229066530352113989013066692570397437773702413957231955020804389634415750498870634142816046788045672568297485242527508630207469164390742003932759774267358556602879306918807555750836800249985550904087271797537215843856934114642382854402532562504961847107385321625601211533133161511192639301728105746220687191517987404378034935607228167440448968116089808516638097060020070846318846918229693351291405338045145821917930096557614039198824684717692434787750244140625 = 5 ^ 4346
answered 49 mins ago
andrew.punnettandrew.punnett
933 bronze badges
New contributor
andrew.punnett is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
2
$begingroup$
While an exact answer does answer the question, exactly how you worked that out would probably be more useful to the person asking the question.
$endgroup$
– Ispil
38 mins ago
add a comment |
$begingroup$
201882615390657491958528733888359303897206738410754045263963565695705442119457224168899440239407953138581226299365782567442925725493850667127823188129261463991440173793523996779651936654389368686597194439736208695989862156299629602332523464076512669290731774513558552819180354651303963581641490360308535552425419867299337653389070510045424468908107895566363643482640162372352948553283421340038905458554369108404396575106064121414101960663718546239386527523409161552124792218268239338974867937280489575854266372435173446464066145926791484234116593481699639727998774125414871721332982942016722814109084246332819815465119939678154783718052333181096038896636579784807212135999682794464880561777058643610122484366550692964046735317370672168782581592297953410438100999375161197662519910850059633016528523568042285302742062098814548246723733888013653327016324124727737686998618632277442820374655493093729902407403246796933589232379520684294387357381354286158732655143619009740514672918111683766211391182403531198532559980151972513489907217185072196731637657634674068559899298805500983571984624086190968818017889989749154302003358764408667797989976730972834651878998380425225936897264605310688663029535576600866502864768965770091351971521995641025227860905919121596849003861094298243892705486363508792818416683489930886591576035182909921868555205172091169698191585767546957494046847024226730833257159854651007706945782566951387958682409697454133730086314492661919431019883237423708525758459729006177183221902634043244036721957840616924771617991861189108596959612503053521704057188513232970211432467080796220044513875134615739794385874670476886205780889353138817697126168129565683692421875294802472389184825853664308097076451463513926649779788130377406299829608329206810680213500593258029567966685039842829425254271550324266936497912430799186821435764991658842175752107255972699604608610838678647922991780897811201255157892448118302260686546980422098465087256649477365011881596878199059608414801013417027677837816041537974933022551966344978889501537172467203506670958637174099226979184380737481324329743693108262765896755437598412730342468865474573477004619362456714144985785078817902129543526158982694832379771931581941839225962375548217493133113050127913932315166413560509241349541568784192095222792848694381349868462030138524690958834727087880318746593234222439280165442150519813234371751409660250721132893912068388675454902832327537395026029852373100586738988362442544910516664069691179659777362156805235491174484504759330371215949360906031780262687660002512614551478392076625118081138080259140457229066530352113989013066692570397437773702413957231955020804389634415750498870634142816046788045672568297485242527508630207469164390742003932759774267358556602879306918807555750836800249985550904087271797537215843856934114642382854402532562504961847107385321625601211533133161511192639301728105746220687191517987404378034935607228167440448968116089808516638097060020070846318846918229693351291405338045145821917930096557614039198824684717692434787750244140625 = 5 ^ 4346
answered 49 mins ago
andrew.punnettandrew.punnett
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$endgroup$
2
$begingroup$
While an exact answer does answer the question, exactly how you worked that out would probably be more useful to the person asking the question.
$endgroup$
– Ispil
38 mins ago
add a comment |
$begingroup$
201882615390657491958528733888359303897206738410754045263963565695705442119457224168899440239407953138581226299365782567442925725493850667127823188129261463991440173793523996779651936654389368686597194439736208695989862156299629602332523464076512669290731774513558552819180354651303963581641490360308535552425419867299337653389070510045424468908107895566363643482640162372352948553283421340038905458554369108404396575106064121414101960663718546239386527523409161552124792218268239338974867937280489575854266372435173446464066145926791484234116593481699639727998774125414871721332982942016722814109084246332819815465119939678154783718052333181096038896636579784807212135999682794464880561777058643610122484366550692964046735317370672168782581592297953410438100999375161197662519910850059633016528523568042285302742062098814548246723733888013653327016324124727737686998618632277442820374655493093729902407403246796933589232379520684294387357381354286158732655143619009740514672918111683766211391182403531198532559980151972513489907217185072196731637657634674068559899298805500983571984624086190968818017889989749154302003358764408667797989976730972834651878998380425225936897264605310688663029535576600866502864768965770091351971521995641025227860905919121596849003861094298243892705486363508792818416683489930886591576035182909921868555205172091169698191585767546957494046847024226730833257159854651007706945782566951387958682409697454133730086314492661919431019883237423708525758459729006177183221902634043244036721957840616924771617991861189108596959612503053521704057188513232970211432467080796220044513875134615739794385874670476886205780889353138817697126168129565683692421875294802472389184825853664308097076451463513926649779788130377406299829608329206810680213500593258029567966685039842829425254271550324266936497912430799186821435764991658842175752107255972699604608610838678647922991780897811201255157892448118302260686546980422098465087256649477365011881596878199059608414801013417027677837816041537974933022551966344978889501537172467203506670958637174099226979184380737481324329743693108262765896755437598412730342468865474573477004619362456714144985785078817902129543526158982694832379771931581941839225962375548217493133113050127913932315166413560509241349541568784192095222792848694381349868462030138524690958834727087880318746593234222439280165442150519813234371751409660250721132893912068388675454902832327537395026029852373100586738988362442544910516664069691179659777362156805235491174484504759330371215949360906031780262687660002512614551478392076625118081138080259140457229066530352113989013066692570397437773702413957231955020804389634415750498870634142816046788045672568297485242527508630207469164390742003932759774267358556602879306918807555750836800249985550904087271797537215843856934114642382854402532562504961847107385321625601211533133161511192639301728105746220687191517987404378034935607228167440448968116089808516638097060020070846318846918229693351291405338045145821917930096557614039198824684717692434787750244140625 = 5 ^ 4346
answered 49 mins ago
andrew.punnettandrew.punnett
933 bronze badges
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$endgroup$
201882615390657491958528733888359303897206738410754045263963565695705442119457224168899440239407953138581226299365782567442925725493850667127823188129261463991440173793523996779651936654389368686597194439736208695989862156299629602332523464076512669290731774513558552819180354651303963581641490360308535552425419867299337653389070510045424468908107895566363643482640162372352948553283421340038905458554369108404396575106064121414101960663718546239386527523409161552124792218268239338974867937280489575854266372435173446464066145926791484234116593481699639727998774125414871721332982942016722814109084246332819815465119939678154783718052333181096038896636579784807212135999682794464880561777058643610122484366550692964046735317370672168782581592297953410438100999375161197662519910850059633016528523568042285302742062098814548246723733888013653327016324124727737686998618632277442820374655493093729902407403246796933589232379520684294387357381354286158732655143619009740514672918111683766211391182403531198532559980151972513489907217185072196731637657634674068559899298805500983571984624086190968818017889989749154302003358764408667797989976730972834651878998380425225936897264605310688663029535576600866502864768965770091351971521995641025227860905919121596849003861094298243892705486363508792818416683489930886591576035182909921868555205172091169698191585767546957494046847024226730833257159854651007706945782566951387958682409697454133730086314492661919431019883237423708525758459729006177183221902634043244036721957840616924771617991861189108596959612503053521704057188513232970211432467080796220044513875134615739794385874670476886205780889353138817697126168129565683692421875294802472389184825853664308097076451463513926649779788130377406299829608329206810680213500593258029567966685039842829425254271550324266936497912430799186821435764991658842175752107255972699604608610838678647922991780897811201255157892448118302260686546980422098465087256649477365011881596878199059608414801013417027677837816041537974933022551966344978889501537172467203506670958637174099226979184380737481324329743693108262765896755437598412730342468865474573477004619362456714144985785078817902129543526158982694832379771931581941839225962375548217493133113050127913932315166413560509241349541568784192095222792848694381349868462030138524690958834727087880318746593234222439280165442150519813234371751409660250721132893912068388675454902832327537395026029852373100586738988362442544910516664069691179659777362156805235491174484504759330371215949360906031780262687660002512614551478392076625118081138080259140457229066530352113989013066692570397437773702413957231955020804389634415750498870634142816046788045672568297485242527508630207469164390742003932759774267358556602879306918807555750836800249985550904087271797537215843856934114642382854402532562504961847107385321625601211533133161511192639301728105746220687191517987404378034935607228167440448968116089808516638097060020070846318846918229693351291405338045145821917930096557614039198824684717692434787750244140625 = 5 ^ 4346
answered 49 mins ago
andrew.punnettandrew.punnett
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edited 16 mins ago
answered 49 mins ago
andrew.punnettandrew.punnett
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answered 49 mins ago
andrew.punnettandrew.punnett
933 bronze badges
answered 49 mins ago
andrew.punnettandrew.punnett
933 bronze badges
933 bronze badges
New contributor
andrew.punnett is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor
andrew.punnett is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
$begingroup$
While an exact answer does answer the question, exactly how you worked that out would probably be more useful to the person asking the question.
$endgroup$
– Ispil
38 mins ago
add a comment |
2
$begingroup$
While an exact answer does answer the question, exactly how you worked that out would probably be more useful to the person asking the question.
$endgroup$
– Ispil
38 mins ago
2
2
$begingroup$
While an exact answer does answer the question, exactly how you worked that out would probably be more useful to the person asking the question.
$endgroup$
– Ispil
38 mins ago
$begingroup$
While an exact answer does answer the question, exactly how you worked that out would probably be more useful to the person asking the question.
$endgroup$
– Ispil
38 mins ago
add a comment |
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$begingroup$
Note: $5^92=2019....$
$endgroup$
– J. W. Tanner
10 hours ago
5
$begingroup$
$5^4364=2.018826153906575ldotscdot 10^3050$.
$endgroup$
– Christian Blatter
10 hours ago