Evaluate log base 0.25 of 16

$\log_{0.25} (16)$

Step 1

Rewrite $\log_{0.25} (16)$ 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 $b = 10$ .

$\frac{\log (16)}{\log (0.25)}$

Step 2

Log base $10$ of $0.25$ is approximately $- 0.60205999$ .

$\frac{\log (16)}{- 0.60205999}$

Step 3

Move the negative in front of the fraction.

$- \frac{\log (16)}{0.60205999}$

Step 4

Log base $10$ of $16$ is approximately $1.20411998$ .

$- \frac{1.20411998}{0.60205999}$

Step 5

Divide $1.20411998$ by $0.60205999$ .

$- 1 \cdot 2$

Step 6

Multiply $- 1$ by $2$ .

$- 2$