Precalculus Examples

$\log (\frac{7 y^{3}}{8 z})$

Step 1

Rewrite $\log (\frac{7 y^{3}}{8 z})$ as $\log (7 y^{3}) - \log (8 z)$ .

$\log (7 y^{3}) - \log (8 z)$

Step 2

Rewrite $\log (7 y^{3})$ as $\log (7) + \log (y^{3})$ .

$\log (7) + \log (y^{3}) - \log (8 z)$

Step 3

Expand $\log (y^{3})$ by moving $3$ outside the logarithm.

$\log (7) + 3 \log (y) - \log (8 z)$

Step 4

Rewrite $\log (8 z)$ as $\log (8) + \log (z)$ .

$\log (7) + 3 \log (y) - (\log (8) + \log (z))$

Step 5

Simplify each term.

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Step 5.1

Simplify each term.

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Step 5.1.1

Rewrite $\log (8)$ as $\log (2^{3})$ .

$\log (7) + 3 \log (y) - (\log (2^{3}) + \log (z))$

Step 5.1.2

Expand $\log (2^{3})$ by moving $3$ outside the logarithm.

$\log (7) + 3 \log (y) - (3 \log (2) + \log (z))$

Step 5.2

Apply the distributive property.

$\log (7) + 3 \log (y) - (3 \log (2)) - \log (z)$

Step 5.3

Multiply $3$ by $- 1$ .

$\log (7) + 3 \log (y) - 3 \log (2) - \log (z)$