How do you find the derivative of $f(x)=Log_5(x)$ ?

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Answer 1 · 2016-07-22T19:48:57

$1/(xln(5))$

We want to get this into natural logs as we know how to differentiate them.

$y = log_5x$

$5^y = x$

$ln(x) = ln(5^y)$

$ln(x) = yln(5) implies y = ln(x)/ln(5)$

So now we have to find

$d/(dx) ((ln(x))/(ln(5)))$

$= 1/(ln(5)) d/(dx)(ln(x))$

$= 1/(ln(5)) * 1/x = 1/(xln(5))$

How do you find the derivative of f(x)=Log_5(x)f(x)=Log_5(x)?