Precalculus Examples

$7^{8} (\log_{7} (8))$

Step 1

Raise $7$ to the power of $8$ .

$5764801 \log_{7} (8)$

Step 2

Rewrite $\log_{7} (8)$ using the change of base formula.

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Step 2.1

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 $0$ .

$5764801 \log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}$

Step 2.2

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

$5764801 \frac{\log (8)}{\log (7)}$

Step 3

Combine $5764801$ and $\frac{\log (8)}{\log (7)}$ .

$\frac{5764801 \log (8)}{\log (7)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{5764801 \log (8)}{\log (7)}$

Decimal Form:

$6160390.64534254$