Find the Exact Value ( log of 64)/( log of 8)

$\frac{\log (64)}{\log (8)}$

Step 1

Rewrite $\log (64)$ as $\log (2^{6})$ .

$\frac{\log (2^{6})}{\log (8)}$

Step 2

Expand $\log (2^{6})$ by moving $6$ outside the logarithm.

$\frac{6 \log (2)}{\log (8)}$

Step 3

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

$\frac{6 \log (2)}{\log (2^{3})}$

Step 4

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

$\frac{6 \log (2)}{3 \log (2)}$

Step 5

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 \log (2)$ .

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

Cancel the common factors.

Factor $3$ out of $3 \log (2)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

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

Cancel the common factor.

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

Divide $2$ by $1$ .

$2$