Precalculus Examples

$\log_{3} (9) + \log_{3} (8)$

Step 1

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

$\log_{3} (9 \cdot 8)$

Step 2

Multiply $9$ by $8$ .

$\log_{3} (72)$

Step 3

Rewrite $\log_{3} (72)$ using the change of base formula.

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Step 3.1

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}$

Step 3.2

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$\frac{\log (72)}{\log (3)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (72)}{\log (3)}$

Decimal Form:

$3.89278926 \dots$