Precalculus Examples

$5 \log (x) - 7 \log (y^{6})$

Step 1

Simplify each term.

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Step 1.1

Simplify $5 \log (x)$ by moving $5$ inside the logarithm.

$\log (x^{5}) - 7 \log (y^{6})$

Step 1.2

Simplify $- 7 \log (y^{6})$ by moving $7$ inside the logarithm.

$\log (x^{5}) - \log ({(y^{6})}^{7})$

Step 1.3

Multiply the exponents in ${(y^{6})}^{7}$ .

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Step 1.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log (x^{5}) - \log (y^{6 \cdot 7})$

Step 1.3.2

Multiply $6$ by $7$ .

$\log (x^{5}) - \log (y^{42})$

Step 2

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

$\log (\frac{x^{5}}{y^{42}})$