Precalculus Examples

$\log_{b} (\frac{x y^{2}}{w^{5} z})$

Step 1

Rewrite $\log_{b} (\frac{x y^{2}}{w^{5} z})$ as $\log_{b} (x y^{2}) - \log_{b} (w^{5} z)$ .

$\log_{b} (x y^{2}) - \log_{b} (w^{5} z)$

Step 2

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

$\log_{b} (x) + \log_{b} (y^{2}) - \log_{b} (w^{5} z)$

Step 3

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

$\log_{b} (x) + 2 \log_{b} (y) - \log_{b} (w^{5} z)$

Step 4

Rewrite $\log_{b} (w^{5} z)$ as $\log_{b} (w^{5}) + \log_{b} (z)$ .

$\log_{b} (x) + 2 \log_{b} (y) - (\log_{b} (w^{5}) + \log_{b} (z))$

Step 5

Expand $\log_{b} (w^{5})$ by moving $5$ outside the logarithm.

$\log_{b} (x) + 2 \log_{b} (y) - (5 \log_{b} (w) + \log_{b} (z))$

Step 6

Simplify each term.

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Step 6.1

Apply the distributive property.

$\log_{b} (x) + 2 \log_{b} (y) - (5 \log_{b} (w)) - \log_{b} (z)$

Step 6.2

Multiply $5$ by $- 1$ .

$\log_{b} (x) + 2 \log_{b} (y) - 5 \log_{b} (w) - \log_{b} (z)$