Precalculus Examples

$\frac{\ln (8)}{\ln (4)}$

Step 1

Rewrite $\ln (8)$ as $\ln (2^{3})$ .

$\frac{\ln (2^{3})}{\ln (4)}$

Step 2

Expand $\ln (2^{3})$ by moving $3$ outside the logarithm.

$\frac{3 \ln (2)}{\ln (4)}$

Step 3

Rewrite $\ln (4)$ as $\ln (2^{2})$ .

$\frac{3 \ln (2)}{\ln (2^{2})}$

Step 4

Expand $\ln (2^{2})$ by moving $2$ outside the logarithm.

$\frac{3 \ln (2)}{2 \ln (2)}$

Step 5

Cancel the common factor of $\ln (2)$ .

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Step 5.1

Cancel the common factor.

$\frac{3 \ln (2)}{2 \ln (2)}$

Step 5.2

Rewrite the expression.

$\frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$