Precalculus Examples

$\frac{\ln (\frac{1}{2.4})}{\frac{\ln (\frac{2.1}{2.4})}{24}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\ln (\frac{1}{2.4}) \frac{24}{\ln (\frac{2.1}{2.4})}$

Step 2

Divide $1$ by $2.4$ .

$\ln (0.41\overline{6}) \frac{24}{\ln (\frac{2.1}{2.4})}$

Step 3

Divide $2.1$ by $2.4$ .

$\ln (0.41\overline{6}) \frac{24}{\ln (0.875)}$

Step 4

Multiply $\ln (0.41\overline{6}) \frac{24}{\ln (0.875)}$ .

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Step 4.1

Combine $\ln (0.41\overline{6})$ and $\frac{24}{\ln (0.875)}$ .

$\frac{\ln (0.41\overline{6}) \cdot 24}{\ln (0.875)}$

Step 4.2

Reorder $\ln (0.41\overline{6})$ and $24$ .

$\frac{24 \cdot \ln (0.41\overline{6})}{\ln (0.875)}$

Step 4.3

Simplify $24 \cdot \ln (0.41\overline{6})$ by moving $24$ inside the logarithm.

$\frac{\ln ({0.41\overline{6}}^{24})}{\ln (0.875)}$

Step 5

Raise $0.41\overline{6}$ to the power of $24$ .

$\frac{\ln (0)}{\ln (0.875)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (0)}{\ln (0.875)}$

Decimal Form:

$157.35063705 \dots$