Algebra Examples

$\log_{7} ({(\frac{1}{2} m^{5})}^{4})$

Step 1

Expand $\log_{7} ({(\frac{1}{2} m^{5})}^{4})$ by moving $4$ outside the logarithm.

$4 \log_{7} (\frac{1}{2} m^{5})$

Step 2

Rewrite $\log_{7} (\frac{1}{2} m^{5})$ as $\log_{7} (\frac{1}{2}) + \log_{7} (m^{5})$ .

$4 (\log_{7} (\frac{1}{2}) + \log_{7} (m^{5}))$

Step 3

Rewrite $\log_{7} (\frac{1}{2})$ as $\log_{7} (1) - \log_{7} (2)$ .

$4 (\log_{7} (1) - \log_{7} (2) + \log_{7} (m^{5}))$

Step 4

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

$4 (\log_{7} (1) - \log_{7} (2) + 5 \log_{7} (m))$

Step 5

Logarithm base $7$ of $1$ is $0$ .

$4 (0 - \log_{7} (2) + 5 \log_{7} (m))$

Step 6

Subtract $\log_{7} (2)$ from $0$ .

$4 (- \log_{7} (2) + 5 \log_{7} (m))$

Step 7

Apply the distributive property.

$4 (- \log_{7} (2)) + 4 (5 \log_{7} (m))$

Step 8

Multiply $- 1$ by $4$ .

$- 4 \log_{7} (2) + 4 (5 \log_{7} (m))$

Step 9

Multiply $5$ by $4$ .

$- 4 \log_{7} (2) + 20 \log_{7} (m)$