Precalculus Examples

$\log_{3} (12) + \log_{3} (11) + 5 \log_{3} (7)$

Step 1

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

$\log_{3} (12 \cdot 11) + 5 \log_{3} (7)$

Step 2

Simplify each term.

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Step 2.1

Multiply $12$ by $11$ .

$\log_{3} (132) + 5 \log_{3} (7)$

Step 2.2

Simplify $5 \log_{3} (7)$ by moving $5$ inside the logarithm.

$\log_{3} (132) + \log_{3} (7^{5})$

Step 2.3

Raise $7$ to the power of $5$ .

$\log_{3} (132) + \log_{3} (16807)$

Step 3

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

$\log_{3} (132 \cdot 16807)$

Step 4

Multiply $132$ by $16807$ .

$\log_{3} (2218524)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log_{3} (2218524)$

Decimal Form:

$13.30073659 \dots$