Check the solution to "What is the derivative of log⁡(x)?"

Kelly Nelson

Answered question

2021-12-20

What is the derivative of

\log (x)

jgardner33v4

Beginner2021-12-21Added 35 answers

That depends on what base you intend.

\log x

is sometimes used for

\log_{10} x, \log_{e} x

and

\log_{2} x

\frac{d}{d x} (\log_{b} x) = \frac{1}{x} \frac{1}{\log_{e} x}

Using,

\ln x = \log_{e} x

we write:

\frac{d}{d x} (\log_{b} x) = \frac{1}{x} \frac{1}{\ln b}

vicki331g8

Beginner2021-12-22Added 37 answers

When the logarithmic function is given by:

f (x) = \log_{b} (x)

The derivative of the logarithmic function is given by:

f^{'} (x) = \frac{1}{x \ln (b)}

x is the function argument.
b is the logarithm base.
ln b is the natural logarithm of b.
For example when:

f (x) = \log_{2} (x)

f^{'} (x) = \frac{1}{x \ln (2)}

RizerMix

Expert2021-12-29Added 656 answers

Thanks for the quick response!

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?