Precalculus Examples

$6 \log (b (q)) - \log (b (r))$

Step 1

Simplify each term.

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Step 1.1

Simplify $6 \log (b q)$ by moving $6$ inside the logarithm.

$\log ({(b q)}^{6}) - \log (b (r))$

Step 1.2

Apply the product rule to $b q$ .

$\log (b^{6} q^{6}) - \log (b r)$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log (\frac{b^{6} q^{6}}{b r})$

Step 3

Cancel the common factor of $b^{6}$ and $b$ .

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Step 3.1

Factor $b$ out of $b^{6} q^{6}$ .

$\log (\frac{b (b^{5} q^{6})}{b r})$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $b$ out of $b r$ .

$\log (\frac{b (b^{5} q^{6})}{b (r)})$

Step 3.2.2

Cancel the common factor.

$\log (\frac{b (b^{5} q^{6})}{b r})$

Step 3.2.3

Rewrite the expression.

$\log (\frac{b^{5} q^{6}}{r})$