Precalculus Examples

$\log_{b} (\frac{8 x z^{6}}{y})$

Step 1

Rewrite $\log_{b} (\frac{8 x z^{6}}{y})$ as $\log_{b} (8 x z^{6}) - \log_{b} (y)$ .

$\log_{b} (8 x z^{6}) - \log_{b} (y)$

Step 2

Rewrite $\log_{b} (8 x z^{6})$ as $\log_{b} (8 x) + \log_{b} (z^{6})$ .

$\log_{b} (8 x) + \log_{b} (z^{6}) - \log_{b} (y)$

Step 3

Rewrite $\log_{b} (8 x)$ as $\log_{b} (8) + \log_{b} (x)$ .

$\log_{b} (8) + \log_{b} (x) + \log_{b} (z^{6}) - \log_{b} (y)$

Step 4

Expand $\log_{b} (z^{6})$ by moving $6$ outside the logarithm.

$\log_{b} (8) + \log_{b} (x) + 6 \log_{b} (z) - \log_{b} (y)$

Step 5

Simplify each term.

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Step 5.1

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

$\log_{b} (2^{3}) + \log_{b} (x) + 6 \log_{b} (z) - \log_{b} (y)$

Step 5.2

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

$3 \log_{b} (2) + \log_{b} (x) + 6 \log_{b} (z) - \log_{b} (y)$