Precalculus Examples

$\frac{\ln (2)}{- \frac{1}{16} \cdot \ln (\frac{19}{51})}$

Step 1

Simplify the denominator.

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Step 1.1

Reorder $\ln (\frac{19}{51})$ and $\frac{1}{16}$ .

$\frac{\ln (2)}{- (\frac{1}{16} \ln (\frac{19}{51}))}$

Step 1.2

Simplify $\frac{1}{16} \ln (\frac{19}{51})$ by moving $\frac{1}{16}$ inside the logarithm.

$\frac{\ln (2)}{- \ln ({(\frac{19}{51})}^{\frac{1}{16}})}$

Step 2

Simplify the expression.

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Step 2.1

Apply the product rule to $\frac{19}{51}$ .

$\frac{\ln (2)}{- \ln (\frac{19^{\frac{1}{16}}}{51^{\frac{1}{16}}})}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{\ln (2)}{\ln (\frac{19^{\frac{1}{16}}}{51^{\frac{1}{16}}})}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{\ln (2)}{\ln (\frac{19^{\frac{1}{16}}}{51^{\frac{1}{16}}})}$

Decimal Form:

$11.23202835 \dots$