Trigonometry Examples

$\log_{3} (48)$

Step 1

Rewrite $\log_{3} (48)$ as $\log_{3} (2^{4} \cdot 3)$ .

$\log_{3} (2^{4} \cdot 3)$

Step 2

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

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

Step 3

Simplify each term.

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Step 3.1

Expand $\log_{3} (2^{4})$ by moving $4$ outside the logarithm.

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

Step 3.2

Logarithm base $3$ of $3$ is $1$ .

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