Precalculus Examples

$\log_{2} (\frac{8 x^{4}}{5})$

Step 1

Rewrite $\log_{2} (\frac{8 x^{4}}{5})$ as $\log_{2} (8 x^{4}) - \log_{2} (5)$ .

$\log_{2} (8 x^{4}) - \log_{2} (5)$

Step 2

Rewrite $\log_{2} (8 x^{4})$ as $\log_{2} (8) + \log_{2} (x^{4})$ .

$\log_{2} (8) + \log_{2} (x^{4}) - \log_{2} (5)$

Step 3

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

$\log_{2} (8) + 4 \log_{2} (x) - \log_{2} (5)$

Step 4

Logarithm base $2$ of $8$ is $3$ .

$3 + 4 \log_{2} (x) - \log_{2} (5)$