Precalculus Examples

$\log (\frac{3 x^{6}}{8 y^{2}})$

Step 1

Rewrite $\log (\frac{3 x^{6}}{8 y^{2}})$ as $\log (3 x^{6}) - \log (8 y^{2})$ .

$\log (3 x^{6}) - \log (8 y^{2})$

Step 2

Rewrite $\log (3 x^{6})$ as $\log (3) + \log (x^{6})$ .

$\log (3) + \log (x^{6}) - \log (8 y^{2})$

Step 3

Expand $\log (x^{6})$ by moving $6$ outside the logarithm.

$\log (3) + 6 \log (x) - \log (8 y^{2})$

Step 4

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

$\log (3) + 6 \log (x) - (\log (8) + \log (y^{2}))$

Step 5

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

$\log (3) + 6 \log (x) - (\log (8) + 2 \log (y))$

Step 6

Simplify each term.

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Step 6.1

Simplify each term.

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Step 6.1.1

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

$\log (3) + 6 \log (x) - (\log (2^{3}) + 2 \log (y))$

Step 6.1.2

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

$\log (3) + 6 \log (x) - (3 \log (2) + 2 \log (y))$

Step 6.2

Apply the distributive property.

$\log (3) + 6 \log (x) - (3 \log (2)) - (2 \log (y))$

Step 6.3

Multiply $3$ by $- 1$ .

$\log (3) + 6 \log (x) - 3 \log (2) - (2 \log (y))$

Step 6.4

Multiply $2$ by $- 1$ .

$\log (3) + 6 \log (x) - 3 \log (2) - 2 \log (y)$