Evaluate 3 log base 3 of 8

$3 \log_{3} (8)$

Step 1

Simplify $3 \log_{3} (8)$ by moving $3$ inside the logarithm.

$\log_{3} (8^{3})$

Step 2

Raise $8$ to the power of $3$ .

$\log_{3} (512)$

Step 3

Rewrite $\log_{3} (512)$ 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 $b = 10$ .

$\frac{\log (512)}{\log (3)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (512)}{\log (3)}$

Decimal Form:

$5.67836778 \dots$