Algebra Examples

$\log_{12} (18) + 3 \cdot \log_{12} (2)$

Step 1

Simplify each term.

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Step 1.1

Simplify $3 \log_{12} (2)$ by moving $3$ inside the logarithm.

$\log_{12} (18) + \log_{12} (2^{3})$

Step 1.2

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

$\log_{12} (18) + \log_{12} (8)$

Step 2

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

$\log_{12} (18 \cdot 8)$

Step 3

Multiply $18$ by $8$ .

$\log_{12} (144)$

Step 4

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

$2$