Evaluate log base 5 of (x/4)^2

$\log_{5} ({(\frac{x}{4})}^{2})$

Step 1

Apply the product rule to $\frac{x}{4}$ .

$\log_{5} (\frac{x^{2}}{4^{2}})$

Step 2

Raise $4$ to the power of $2$ .

$\log_{5} (\frac{x^{2}}{16})$

Step 3

Rewrite $\log_{5} (\frac{x^{2}}{16})$ 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 $b = 10$ .

$\frac{\log (\frac{x^{2}}{16})}{\log (5)}$