Precalculus Examples

$2 \log_{4} (8 x^{3} y)$

Step 1

Rewrite $\log_{4} (8 x^{3} y)$ as $\log_{4} (8 x^{3}) + \log_{4} (y)$ .

$2 (\log_{4} (8 x^{3}) + \log_{4} (y))$

Step 2

Rewrite $\log_{4} (8 x^{3})$ as $\log_{4} (8) + \log_{4} (x^{3})$ .

$2 (\log_{4} (8) + \log_{4} (x^{3}) + \log_{4} (y))$

Step 3

Expand $\log_{4} (x^{3})$ by moving $3$ outside the logarithm.

$2 (\log_{4} (8) + 3 \log_{4} (x) + \log_{4} (y))$

Step 4

Logarithm base $4$ of $8$ is $\frac{3}{2}$ .

$2 (\frac{3}{2} + 3 \log_{4} (x) + \log_{4} (y))$

Step 5

Apply the distributive property.

$2 (\frac{3}{2}) + 2 (3 \log_{4} (x)) + 2 \log_{4} (y)$

Step 6

Simplify.

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Step 6.1

Cancel the common factor of $2$ .

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Step 6.1.1

Cancel the common factor.

$2 (\frac{3}{2}) + 2 (3 \log_{4} (x)) + 2 \log_{4} (y)$

Step 6.1.2

Rewrite the expression.

$3 + 2 (3 \log_{4} (x)) + 2 \log_{4} (y)$

Step 6.2

Multiply $3$ by $2$ .

$3 + 6 \log_{4} (x) + 2 \log_{4} (y)$