Precalculus Examples

$\log_{3} (189) - \log_{3} (7)$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\log_{3} (189)$ as $\log_{3} (3^{3} \cdot 7)$ .

$\log_{3} (3^{3} \cdot 7) - \log_{3} (7)$

Step 1.2

Rewrite $\log_{3} (3^{3} \cdot 7)$ as $\log_{3} (3^{3}) + \log_{3} (7)$ .

$\log_{3} (3^{3}) + \log_{3} (7) - \log_{3} (7)$

Step 1.3

Use logarithm rules to move $3$ out of the exponent.

$3 \log_{3} (3) + \log_{3} (7) - \log_{3} (7)$

Step 1.4

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

$3 \cdot 1 + \log_{3} (7) - \log_{3} (7)$

Step 1.5

Multiply $3$ by $1$ .

$3 + \log_{3} (7) - \log_{3} (7)$

Step 2

Subtract $\log_{3} (7)$ from $\log_{3} (7)$ .

$3 + 0$

Step 3

Add $3$ and $0$ .

$3$