Precalculus Examples

$\log_{3} (\frac{405}{x})$

Step 1

Rewrite $\log_{3} (\frac{405}{x})$ as $\log_{3} (405) - \log_{3} (x)$ .

$\log_{3} (405) - \log_{3} (x)$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\log_{3} (405)$ as $\log_{3} (3^{4} \cdot 5)$ .

$\log_{3} (3^{4} \cdot 5) - \log_{3} (x)$

Step 2.2

Rewrite $\log_{3} (3^{4} \cdot 5)$ as $\log_{3} (3^{4}) + \log_{3} (5)$ .

$\log_{3} (3^{4}) + \log_{3} (5) - \log_{3} (x)$

Step 2.3

Use logarithm rules to move $4$ out of the exponent.

$4 \log_{3} (3) + \log_{3} (5) - \log_{3} (x)$

Step 2.4

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

$4 \cdot 1 + \log_{3} (5) - \log_{3} (x)$

Step 2.5

Multiply $4$ by $1$ .

$4 + \log_{3} (5) - \log_{3} (x)$