Evaluate ( log base 4 of x)/( log base 4 of 4)

$\frac{\log_{4} (x)}{\log_{4} (4)}$

Step 1

Logarithm base $4$ of $4$ is $1$ .

$\frac{\log_{4} (x)}{1}$

Step 2

Divide $\log_{4} (x)$ by $1$ .

$\log_{4} (x)$

Step 3

Rewrite $\log_{4} (x)$ 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 $b = 10$ .

$\frac{\log (x)}{\log (4)}$