Precalculus Examples

$\log_{7} (\frac{{(2 x - 1)}^{5} {(x + 1)}^{2}}{{(3 x - 2)}^{3}})$

Step 1

Rewrite $\log_{7} (\frac{{(2 x - 1)}^{5} {(x + 1)}^{2}}{{(3 x - 2)}^{3}})$ as $\log_{7} ({(2 x - 1)}^{5} {(x + 1)}^{2}) - \log_{7} ({(3 x - 2)}^{3})$ .

$\log_{7} ({(2 x - 1)}^{5} {(x + 1)}^{2}) - \log_{7} ({(3 x - 2)}^{3})$

Step 2

Expand $\log_{7} ({(3 x - 2)}^{3})$ by moving $3$ outside the logarithm.

$\log_{7} ({(2 x - 1)}^{5} {(x + 1)}^{2}) - (3 \log_{7} (3 x - 2))$

Step 3

Multiply $3$ by $- 1$ .

$\log_{7} ({(2 x - 1)}^{5} {(x + 1)}^{2}) - 3 \log_{7} (3 x - 2)$

Step 4

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

$\log_{7} ({(2 x - 1)}^{5}) + \log_{7} ({(x + 1)}^{2}) - 3 \log_{7} (3 x - 2)$

Step 5

Expand $\log_{7} ({(2 x - 1)}^{5})$ by moving $5$ outside the logarithm.

$5 \log_{7} (2 x - 1) + \log_{7} ({(x + 1)}^{2}) - 3 \log_{7} (3 x - 2)$

Step 6

Expand $\log_{7} ({(x + 1)}^{2})$ by moving $2$ outside the logarithm.

$5 \log_{7} (2 x - 1) + 2 \log_{7} (x + 1) - 3 \log_{7} (3 x - 2)$