Precalculus Examples

$\log_{7} (\frac{x^{5}}{4})$

Step 1

Rewrite $\log_{7} (\frac{x^{5}}{4})$ as $\log_{7} (x^{5}) - \log_{7} (4)$ .

$\log_{7} (x^{5}) - \log_{7} (4)$

Step 2

Expand $\log_{7} (x^{5})$ by moving $5$ outside the logarithm.

$5 \log_{7} (x) - \log_{7} (4)$

Step 3

Rewrite $\log_{7} (4)$ as $\log_{7} (2^{2})$ .

$5 \log_{7} (x) - \log_{7} (2^{2})$

Step 4

Expand $\log_{7} (2^{2})$ by moving $2$ outside the logarithm.

$5 \log_{7} (x) - (2 \log_{7} (2))$

Step 5

Multiply $2$ by $- 1$ .

$5 \log_{7} (x) - 2 \log_{7} (2)$