Precalculus Examples

$\log_{2} (\frac{1}{32 x^{4}})$

Step 1

Rewrite $\log_{2} (\frac{1}{32 x^{4}})$ as $\log_{2} (1) - \log_{2} (32 x^{4})$ .

$\log_{2} (1) - \log_{2} (32 x^{4})$

Step 2

Logarithm base $2$ of $1$ is $0$ .

$0 - \log_{2} (32 x^{4})$

Step 3

Subtract $\log_{2} (32 x^{4})$ from $0$ .

$- \log_{2} (32 x^{4})$

Step 4

Rewrite $\log_{2} (32 x^{4})$ as $\log_{2} (32) + \log_{2} (x^{4})$ .

$- (\log_{2} (32) + \log_{2} (x^{4}))$

Step 5

Expand $\log_{2} (x^{4})$ by moving $4$ outside the logarithm.

$- (\log_{2} (32) + 4 \log_{2} (x))$

Step 6

Logarithm base $2$ of $32$ is $5$ .

$- (5 + 4 \log_{2} (x))$

Step 7

Apply the distributive property.

$- 1 \cdot 5 - (4 \log_{2} (x))$

Step 8

Multiply $- 1$ by $5$ .

$- 5 - (4 \log_{2} (x))$

Step 9

Multiply $4$ by $- 1$ .

$- 5 - 4 \log_{2} (x)$