Calculus Examples

$8 \log_{8} (19)$

Step 1

Simplify $8 \log_{8} (19)$ by moving $8$ inside the logarithm.

$\log_{8} (19^{8})$

Step 2

Raise $19$ to the power of $8$ .

$\log_{8} (16983563041)$

Step 3

Rewrite $\log_{8} (16983563041)$ using the change of base formula.

Tap for more steps...

Step 3.1

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 $0$ .

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

Step 3.2

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

$\frac{\log (16983563041)}{\log (8)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (16983563041)}{\log (8)}$

Decimal Form:

$11.32780670 \dots$