Evaluate ( log base 9 of m)/( log of m)

$\frac{\log_{9} (m)}{\log (m)}$

Rewrite $\log_{9} (m)$ 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 $0$ .

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

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

$\frac{\frac{\log (m)}{\log (9)}}{\log (m)}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{\log (m)}{\log (9)} \cdot \frac{1}{\log (m)}$

Cancel the common factor of $\log (m)$ .

Cancel the common factor.

$\frac{\log (m)}{\log (9)} \cdot \frac{1}{\log (m)}$

Rewrite the expression.

$\frac{1}{\log (9)}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{\log (9)}$

Decimal Form:

$1.04795163 \dots$