Precalculus Examples

$6 \log_{9} (x) - \log_{9} (z) - 2 \log_{9} (y)$

Step 1

Simplify each term.

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Step 1.1

Simplify $6 \log_{9} (x)$ by moving $6$ inside the logarithm.

$\log_{9} (x^{6}) - \log_{9} (z) - 2 \log_{9} (y)$

Step 1.2

Simplify $- 2 \log_{9} (y)$ by moving $2$ inside the logarithm.

$\log_{9} (x^{6}) - \log_{9} (z) - \log_{9} (y^{2})$

Step 2

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

$\log_{9} (\frac{x^{6}}{z}) - \log_{9} (y^{2})$

Step 3

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

$\log_{9} (\frac{\frac{x^{6}}{z}}{y^{2}})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\log_{9} (\frac{x^{6}}{z} \cdot \frac{1}{y^{2}})$

Step 5

Combine.

$\log_{9} (\frac{x^{6} \cdot 1}{z y^{2}})$

Step 6

Multiply $x^{6}$ by $1$ .

$\log_{9} (\frac{x^{6}}{z y^{2}})$