Algebra Examples

$5 \log_{b} (x) + 9 \log_{b} (y) - 3 \log_{b} (z)$

Step 1

Simplify each term.

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Step 1.1

Simplify $5 \log_{b} (x)$ by moving $5$ inside the logarithm.

$\log_{b} (x^{5}) + 9 \log_{b} (y) - 3 \log_{b} (z)$

Step 1.2

Simplify $9 \log_{b} (y)$ by moving $9$ inside the logarithm.

$\log_{b} (x^{5}) + \log_{b} (y^{9}) - 3 \log_{b} (z)$

Step 1.3

Simplify $- 3 \log_{b} (z)$ by moving $3$ inside the logarithm.

$\log_{b} (x^{5}) + \log_{b} (y^{9}) - \log_{b} (z^{3})$

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{b} (x^{5} y^{9}) - \log_{b} (z^{3})$

Step 3

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{b} (\frac{x^{5} y^{9}}{z^{3}})$