Evaluate log base 5 of 1/4

$\log_{5} (\frac{1}{4})$

Step 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 2

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

$\frac{\log (\frac{1}{4})}{\log (5)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (\frac{1}{4})}{\log (5)}$

Decimal Form:

$- 0.86135311 \dots$