logarithmic rules with functionsLogarithmic expression with three termsQuestion regarding differentiating logarithmic functionsHow to bound this difference between two logarithmic expressionIs this manipulation with logs allowed?Multi-valued logarithmic functionRoot of Logarithmic EquationComparing functions that have logs in exponentsFinding the domain of logarithmic functionLinear functions versus Logarithmic and Exponential functionschange to logarithmic form. solve for P.
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logarithmic rules with functions
Logarithmic expression with three termsQuestion regarding differentiating logarithmic functionsHow to bound this difference between two logarithmic expressionIs this manipulation with logs allowed?Multi-valued logarithmic functionRoot of Logarithmic EquationComparing functions that have logs in exponentsFinding the domain of logarithmic functionLinear functions versus Logarithmic and Exponential functionschange to logarithmic form. solve for P.
$begingroup$
Do the logarithmic rules work when taking logs of functions as opposed to numbers?
i.e. suppose $f$ is a function and n is a number, is $log (f(x)^n) = n · log(f)$
logarithms
edited 8 hours ago
Bernard
127k743121
asked 8 hours ago
JessJess
135111
$endgroup$
add a comment |
$begingroup$
Do the logarithmic rules work when taking logs of functions as opposed to numbers?
i.e. suppose $f$ is a function and n is a number, is $log (f(x)^n) = n · log(f)$
logarithms
edited 8 hours ago
Bernard
127k743121
asked 8 hours ago
JessJess
135111
$endgroup$
3
$begingroup$
Of course, because the equality is true for any specific $x$.
$endgroup$
– Mark
8 hours ago
1
$begingroup$
@Mark : What you have said is meaningless. Can you elaborate?
$endgroup$
– MPW
8 hours ago
1
$begingroup$
Why is it meaningless? Put any constant $x$ and you will get an equality. Two functions are equal if they are equal at all points.
$endgroup$
– Mark
8 hours ago
2
$begingroup$
Okay, I guess I understand what you mean. Note that, unfortunately, OP has omitted any mention of $x$ on the RHS.
$endgroup$
– MPW
8 hours ago
add a comment |
$begingroup$
Do the logarithmic rules work when taking logs of functions as opposed to numbers?
i.e. suppose $f$ is a function and n is a number, is $log (f(x)^n) = n · log(f)$
logarithms
edited 8 hours ago
Bernard
127k743121
asked 8 hours ago
JessJess
135111
$endgroup$
Do the logarithmic rules work when taking logs of functions as opposed to numbers?
i.e. suppose $f$ is a function and n is a number, is $log (f(x)^n) = n · log(f)$
logarithms
logarithms
edited 8 hours ago
Bernard
127k743121
asked 8 hours ago
JessJess
135111
edited 8 hours ago
Bernard
127k743121
asked 8 hours ago
JessJess
135111
edited 8 hours ago
Bernard
127k743121
edited 8 hours ago
Bernard
127k743121
edited 8 hours ago
Bernard
127k743121
127k743121
asked 8 hours ago
JessJess
135111
asked 8 hours ago
JessJess
135111
asked 8 hours ago
JessJess
135111
135111
3
$begingroup$
Of course, because the equality is true for any specific $x$.
$endgroup$
– Mark
8 hours ago
1
$begingroup$
@Mark : What you have said is meaningless. Can you elaborate?
$endgroup$
– MPW
8 hours ago
1
$begingroup$
Why is it meaningless? Put any constant $x$ and you will get an equality. Two functions are equal if they are equal at all points.
$endgroup$
– Mark
8 hours ago
2
$begingroup$
Okay, I guess I understand what you mean. Note that, unfortunately, OP has omitted any mention of $x$ on the RHS.
$endgroup$
– MPW
8 hours ago
add a comment |
3
$begingroup$
Of course, because the equality is true for any specific $x$.
$endgroup$
– Mark
8 hours ago
1
$begingroup$
@Mark : What you have said is meaningless. Can you elaborate?
$endgroup$
– MPW
8 hours ago
1
$begingroup$
Why is it meaningless? Put any constant $x$ and you will get an equality. Two functions are equal if they are equal at all points.
$endgroup$
– Mark
8 hours ago
2
$begingroup$
Okay, I guess I understand what you mean. Note that, unfortunately, OP has omitted any mention of $x$ on the RHS.
$endgroup$
– MPW
8 hours ago
3
3
$begingroup$
Of course, because the equality is true for any specific $x$.
$endgroup$
– Mark
8 hours ago
$begingroup$
Of course, because the equality is true for any specific $x$.
$endgroup$
– Mark
8 hours ago
1
1
$begingroup$
@Mark : What you have said is meaningless. Can you elaborate?
$endgroup$
– MPW
8 hours ago
$begingroup$
@Mark : What you have said is meaningless. Can you elaborate?
$endgroup$
– MPW
8 hours ago
1
1
$begingroup$
Why is it meaningless? Put any constant $x$ and you will get an equality. Two functions are equal if they are equal at all points.
$endgroup$
– Mark
8 hours ago
$begingroup$
Why is it meaningless? Put any constant $x$ and you will get an equality. Two functions are equal if they are equal at all points.
$endgroup$
– Mark
8 hours ago
2
2
$begingroup$
Okay, I guess I understand what you mean. Note that, unfortunately, OP has omitted any mention of $x$ on the RHS.
$endgroup$
– MPW
8 hours ago
$begingroup$
Okay, I guess I understand what you mean. Note that, unfortunately, OP has omitted any mention of $x$ on the RHS.
$endgroup$
– MPW
8 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Yes it will work.
$$log(f(x)^n) = log(f(x)times f(x) ... times f(x)$$
$$= log(f(x)) +log(f(x)) + ... +log(f(x))$$
$$=n times log(f(x))$$
answered 8 hours ago
VizagVizag
2,7711518
$endgroup$
add a comment |
$begingroup$
Yes, of course.
Because $f(x)$ is still a number for any $x$.
It even works on expressions: for example $log((x^2+3)^9)=9log(x^2+3).$
answered 8 hours ago
Saketh MalyalaSaketh Malyala
10.2k1637
$endgroup$
add a comment |
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2 Answers
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2 Answers
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$begingroup$
Yes it will work.
$$log(f(x)^n) = log(f(x)times f(x) ... times f(x)$$
$$= log(f(x)) +log(f(x)) + ... +log(f(x))$$
$$=n times log(f(x))$$
answered 8 hours ago
VizagVizag
2,7711518
$endgroup$
add a comment |
$begingroup$
Yes it will work.
$$log(f(x)^n) = log(f(x)times f(x) ... times f(x)$$
$$= log(f(x)) +log(f(x)) + ... +log(f(x))$$
$$=n times log(f(x))$$
answered 8 hours ago
VizagVizag
2,7711518
$endgroup$
add a comment |
$begingroup$
Yes it will work.
$$log(f(x)^n) = log(f(x)times f(x) ... times f(x)$$
$$= log(f(x)) +log(f(x)) + ... +log(f(x))$$
$$=n times log(f(x))$$
answered 8 hours ago
VizagVizag
2,7711518
$endgroup$
Yes it will work.
$$log(f(x)^n) = log(f(x)times f(x) ... times f(x)$$
$$= log(f(x)) +log(f(x)) + ... +log(f(x))$$
$$=n times log(f(x))$$
answered 8 hours ago
VizagVizag
2,7711518
answered 8 hours ago
VizagVizag
2,7711518
answered 8 hours ago
VizagVizag
2,7711518
answered 8 hours ago
VizagVizag
2,7711518
2,7711518
add a comment |
add a comment |
$begingroup$
Yes, of course.
Because $f(x)$ is still a number for any $x$.
It even works on expressions: for example $log((x^2+3)^9)=9log(x^2+3).$
answered 8 hours ago
Saketh MalyalaSaketh Malyala
10.2k1637
$endgroup$
add a comment |
$begingroup$
Yes, of course.
Because $f(x)$ is still a number for any $x$.
It even works on expressions: for example $log((x^2+3)^9)=9log(x^2+3).$
answered 8 hours ago
Saketh MalyalaSaketh Malyala
10.2k1637
$endgroup$
add a comment |
$begingroup$
Yes, of course.
Because $f(x)$ is still a number for any $x$.
It even works on expressions: for example $log((x^2+3)^9)=9log(x^2+3).$
answered 8 hours ago
Saketh MalyalaSaketh Malyala
10.2k1637
$endgroup$
Yes, of course.
Because $f(x)$ is still a number for any $x$.
It even works on expressions: for example $log((x^2+3)^9)=9log(x^2+3).$
answered 8 hours ago
Saketh MalyalaSaketh Malyala
10.2k1637
answered 8 hours ago
Saketh MalyalaSaketh Malyala
10.2k1637
answered 8 hours ago
Saketh MalyalaSaketh Malyala
10.2k1637
answered 8 hours ago
Saketh MalyalaSaketh Malyala
10.2k1637
10.2k1637
add a comment |
add a comment |
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3
$begingroup$
Of course, because the equality is true for any specific $x$.
$endgroup$
– Mark
8 hours ago
1
$begingroup$
@Mark : What you have said is meaningless. Can you elaborate?
$endgroup$
– MPW
8 hours ago
1
$begingroup$
Why is it meaningless? Put any constant $x$ and you will get an equality. Two functions are equal if they are equal at all points.
$endgroup$
– Mark
8 hours ago
2
$begingroup$
Okay, I guess I understand what you mean. Note that, unfortunately, OP has omitted any mention of $x$ on the RHS.
$endgroup$
– MPW
8 hours ago