Evaluate ( log base c of 6)/( log of 6)

$\frac{\log_{c} (6)}{\log (6)}$

Step 1

Rewrite $\log_{c} (6)$ 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 $0$ .

$\frac{\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}}{\log (6)}$

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

$\frac{\frac{\log (6)}{\log (c)}}{\log (6)}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{\log (6)}{\log (c)} \cdot \frac{1}{\log (6)}$

Step 3

Cancel the common factor of $\log (6)$ .

Cancel the common factor.

$\frac{\log (6)}{\log (c)} \cdot \frac{1}{\log (6)}$

Rewrite the expression.

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