Evaluate 9 log base 9 of 7

$9 \log_{9} (7)$

Step 1

Simplify $9 \log_{9} (7)$ by moving $9$ inside the logarithm.

$\log_{9} (7^{9})$

Step 2

Raise $7$ to the power of $9$ .

$\log_{9} (40353607)$

Step 3

Rewrite $\log_{9} (40353607)$ 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 $0$ .

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

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

$\frac{\log (40353607)}{\log (9)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (40353607)}{\log (9)}$

Decimal Form:

$7.97059687 \dots$