Precalculus Examples

$\log_{16} (\frac{2}{3}) + \log_{16} (96)$

Step 1

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

$\log_{16} (\frac{2}{3} \cdot 96)$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Factor $3$ out of $96$ .

$\log_{16} (\frac{2}{3} \cdot (3 (32)))$

Step 2.2

Cancel the common factor.

$\log_{16} (\frac{2}{3} \cdot (3 \cdot 32))$

Step 2.3

Rewrite the expression.

$\log_{16} (2 \cdot 32)$

Step 3

Multiply $2$ by $32$ .

$\log_{16} (64)$

Step 4

Logarithm base $16$ of $64$ is $\frac{3}{2}$ .

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Step 4.1

Factor $2$ out of $6$ .

$\frac{2 (3)}{4}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $4$ .

$\frac{2 \cdot 3}{2 \cdot 2}$

Step 4.2.2

Cancel the common factor.

$\frac{2 \cdot 3}{2 \cdot 2}$

Step 4.2.3

Rewrite the expression.

$\frac{3}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$