Precalculus Examples

$\log_{4} (6 x^{4})$

Step 1

Rewrite $\log_{4} (6 x^{4})$ as $\log_{4} (6) + \log_{4} (x^{4})$ .

$\log_{4} (6) + \log_{4} (x^{4})$

Step 2

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

$\log_{4} (6) + 4 \log_{4} (x)$

Step 3

Simplify each term.

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Step 3.1

Rewrite $\log_{4} (6)$ as $\log_{4} (2 (3))$ .

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

Step 3.2

Rewrite $\log_{4} (2 (3))$ as $\log_{4} (2) + \log_{4} (3)$ .

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

Step 3.3

Logarithm base $4$ of $2$ is $\frac{1}{2}$ .

$\frac{1}{2} + \log_{4} (3) + 4 \log_{4} (x)$