Question

prove that the derivative of log x base a equal to1/(a log x)

Answer 1

\[y = log_ax\]
\[->a^y=x\]
the natural logarithm of both sides
\[\ln a^y = \ln x\]
rearrange
\[y\ln a = \ln x\]
implicit differentiation
\[\ln ay^'\ = \frac{1}{x}\]
\[y^'=\frac{1}{x\ln a}\]