Precalculus Examples

$\log_{9} (18) + \log_{9} (36) - 3 \log_{9} (2)$

Step 1

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

$\log_{9} (18 \cdot 36) - 3 \log_{9} (2)$

Step 2

Simplify each term.

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Step 2.1

Multiply $18$ by $36$ .

$\log_{9} (648) - 3 \log_{9} (2)$

Step 2.2

Simplify $- 3 \log_{9} (2)$ by moving $3$ inside the logarithm.

$\log_{9} (648) - \log_{9} (2^{3})$

Step 2.3

Raise $2$ to the power of $3$ .

$\log_{9} (648) - \log_{9} (8)$

Step 3

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

$\log_{9} (\frac{648}{8})$

Step 4

Logarithm base $9$ of $\frac{648}{8}$ is $2$ .

$2$