Precalculus Examples

$\log_{12} (9) + \log_{12} (16 x) - \log_{12} (x)$

Step 1

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

$\log_{12} (9 (16 x)) - \log_{12} (x)$

Step 2

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

$\log_{12} (\frac{9 (16 x)}{x})$

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

$\log_{12} (\frac{9 (16 x)}{x})$

Step 3.2

Divide $9 \cdot (16)$ by $1$ .

$\log_{12} (9 \cdot (16))$

Step 4

Simplify the expression.

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Step 4.1

Multiply $9$ by $16$ .

$\log_{12} (144)$

Step 4.2

Logarithm base $12$ of $144$ is $2$ .

$2$