Expand the Logarithmic Expression log base 4 of 64/(a(b-1))

$\log_{4} (\frac{64}{a (b - 1)})$

Step 1

Rewrite $\log_{4} (\frac{64}{a (b - 1)})$ as $\log_{4} (64) - \log_{4} (a (b - 1))$ .

$\log_{4} (64) - \log_{4} (a (b - 1))$

Step 2

Logarithm base $4$ of $64$ is $3$ .

$3 - \log_{4} (a (b - 1))$

Step 3

Rewrite $\log_{4} (a (b - 1))$ as $\log_{4} (a) + \log_{4} (b - 1)$ .

$3 - (\log_{4} (a) + \log_{4} (b - 1))$

Step 4

Apply the distributive property.

$3 - \log_{4} (a) - \log_{4} (b - 1)$