Precalculus Examples

$\log_{b} (\frac{14}{3 b})$

Step 1

Rewrite $\log_{b} (\frac{14}{3 b})$ as $\log_{b} (14) - \log_{b} (3 b)$ .

$\log_{b} (14) - \log_{b} (3 b)$

Step 2

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

$\log_{b} (14) - (\log_{b} (3) + \log_{b} (b))$

Step 3

Logarithm base $b$ of $b$ is $1$ .

$\log_{b} (14) - (\log_{b} (3) + 1)$

Step 4

Simplify each term.

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Step 4.1

Rewrite $\log_{b} (14)$ as $\log_{b} (2 (7))$ .

$\log_{b} (2 (7)) - (\log_{b} (3) + 1)$

Step 4.2

Rewrite $\log_{b} (2 (7))$ as $\log_{b} (2) + \log_{b} (7)$ .

$\log_{b} (2) + \log_{b} (7) - (\log_{b} (3) + 1)$

Step 4.3

Apply the distributive property.

$\log_{b} (2) + \log_{b} (7) - \log_{b} (3) - 1 \cdot 1$

Step 4.4

Multiply $- 1$ by $1$ .

$\log_{b} (2) + \log_{b} (7) - \log_{b} (3) - 1$