Precalculus Examples

$\log_{0.25} (3)$

Step 1

Rewrite $\log_{0.25} (3)$ using the change of base formula.

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Step 1.1

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 1.2

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

$\frac{\log (3)}{\log (0.25)}$

Step 2

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

$\frac{\log (3)}{- 0.60205999}$

Step 3

Move the negative in front of the fraction.

$- \frac{\log (3)}{0.60205999}$

Step 4

Log base $10$ of $3$ is approximately $0.47712125$ .

$- \frac{0.47712125}{0.60205999}$

Step 5

Divide $0.47712125$ by $0.60205999$ .

$- 1 \cdot 0.79248125$

Step 6

Multiply $- 1$ by $0.79248125$ .

$- 0.79248125$