Evaluate log base 4 of (16)^100

$\log_{4} ({(16)}^{100})$

Step 1

Remove parentheses.

$\log_{4} (16^{100})$

Step 2

Rewrite $\log_{4} (16^{100})$ 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 $b = 10$ .

$\frac{\log (16^{100})}{\log (4)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (16^{100})}{\log (4)}$

Decimal Form:

$200$