Precalculus Examples

$\frac{\ln (0.09)}{\frac{1}{5} \cdot \ln (\frac{1}{2})}$

Step 1

Simplify $\frac{1}{5} \ln (\frac{1}{2})$ by moving $\frac{1}{5}$ inside the logarithm.

$\frac{\ln (0.09)}{\ln ({(\frac{1}{2})}^{\frac{1}{5}})}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $\frac{1}{2}$ .

$\frac{\ln (0.09)}{\ln (\frac{1^{\frac{1}{5}}}{2^{\frac{1}{5}}})}$

Step 2.2

One to any power is one.

$\frac{\ln (0.09)}{\ln (\frac{1}{2^{\frac{1}{5}}})}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (0.09)}{\ln (\frac{1}{2^{\frac{1}{5}}})}$

Decimal Form:

$17.36965594 \dots$