Evaluate ( log of 8)/( log of 4)

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

Cancel the common factor.

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

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:

$1 \frac{1}{2}$