How do you differentiate $f(x) = log_x (3)$ ?

Question

1868 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-29T14:10:20

There are several ways to do this.

Method 1
Use change of base to write

$f(x) = ln3/lnx = ln3(lnx)^-1$

Now differentiate using the power and chain rules.

Method 2

$y = log_x3$ $hArr$ $x^y=3$ $hArr$ $ylnx=ln3$

Now differentiate implicitly.

Method 3

Use $f(x) = log_x3=1/log_3x = (log_3x)^-1$

Differentiate using the power and chain rules and derivative of logarithms with bases other than $e$ .

$f'(x) = -1/(log_x3)^2*1/(xln3)$

How do you differentiate f(x) = log_x (3)f(x) = log_x (3)?