Evaluate 1/( log base 3 of m)

$\frac{1}{\log_{3} (m)}$

Step 1

Rewrite $\log_{3} (m)$ using the change of base formula.

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$\frac{1}{\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}}$

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$\frac{1}{\frac{\log (m)}{\log (3)}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{\log (3)}{\log (m)}$

Step 3

Multiply $\frac{\log (3)}{\log (m)}$ by $1$ .

$\frac{\log (3)}{\log (m)}$