Precalculus Examples

$\log (\frac{7 x^{3}}{y z^{2}})$

Step 1

Rewrite $\log (\frac{7 x^{3}}{y z^{2}})$ as $\log (7 x^{3}) - \log (y z^{2})$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Rewrite $\log (y z^{2})$ as $\log (y) + \log (z^{2})$ .

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

Step 5

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

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

Step 6

Simplify each term.

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Step 6.1

Apply the distributive property.

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

Step 6.2

Multiply $2$ by $- 1$ .

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