Evaluate log of a* log base a of 5

$\log (a) \cdot \log_{a} (5)$

Rewrite $\log_{a} (5)$ 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 $0$ .

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

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

$\log (a) \frac{\log (5)}{\log (a)}$

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

Cancel the common factor.

$\log (a) \frac{\log (5)}{\log (a)}$

Rewrite the expression.

$\log (5)$

The result can be shown in multiple forms.

Exact Form:

$\log (5)$

Decimal Form:

$0.69897000 \dots$