Precalculus Examples

$2 \log_{7} (\frac{x y^{2}}{z^{4}})$

Step 1

Rewrite $\log_{7} (\frac{x y^{2}}{z^{4}})$ as $\log_{7} (x y^{2}) - \log_{7} (z^{4})$ .

$2 (\log_{7} (x y^{2}) - \log_{7} (z^{4}))$

Step 2

Expand $\log_{7} (z^{4})$ by moving $4$ outside the logarithm.

$2 (\log_{7} (x y^{2}) - (4 \log_{7} (z)))$

Step 3

Multiply $4$ by $- 1$ .

$2 (\log_{7} (x y^{2}) - 4 \log_{7} (z))$

Step 4

Rewrite $\log_{7} (x y^{2})$ as $\log_{7} (x) + \log_{7} (y^{2})$ .

$2 (\log_{7} (x) + \log_{7} (y^{2}) - 4 \log_{7} (z))$

Step 5

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

$2 (\log_{7} (x) + 2 \log_{7} (y) - 4 \log_{7} (z))$

Step 6

Apply the distributive property.

$2 \log_{7} (x) + 2 (2 \log_{7} (y)) + 2 (- 4 \log_{7} (z))$

Step 7

Simplify.

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Step 7.1

Multiply $2$ by $2$ .

$2 \log_{7} (x) + 4 \log_{7} (y) + 2 (- 4 \log_{7} (z))$

Step 7.2

Multiply $- 4$ by $2$ .

$2 \log_{7} (x) + 4 \log_{7} (y) - 8 \log_{7} (z)$