Precalculus Examples

$\log_{0.5} (\frac{1}{25}) \cdot \log_{12} (144)$

Step 1

Logarithm base $12$ of $144$ is $2$ .

$\log_{0.5} (\frac{1}{25}) \cdot 2$

Step 2

Multiply $\log_{0.5} (\frac{1}{25}) \cdot 2$ .

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Step 2.1

Reorder $\log_{0.5} (\frac{1}{25})$ and $2$ .

$2 \cdot \log_{0.5} (\frac{1}{25})$

Step 2.2

Simplify $2 \cdot \log_{0.5} (\frac{1}{25})$ by moving $2$ inside the logarithm.

$\log_{0.5} ({(\frac{1}{25})}^{2})$

Step 3

Apply the product rule to $\frac{1}{25}$ .

$\log_{0.5} (\frac{1^{2}}{25^{2}})$

Step 4

One to any power is one.

$\log_{0.5} (\frac{1}{25^{2}})$

Step 5

Raise $25$ to the power of $2$ .

$\log_{0.5} (\frac{1}{625})$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\log_{0.5} (\frac{1}{625})$

Decimal Form:

$9.28771237 \dots$