Precalculus Examples

$\frac{1}{6} \cdot \log_{c} (x^{7}) - \log_{c} (y^{6} z^{5})$

Step 1

Simplify each term.

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Step 1.1

Simplify $\frac{1}{6} \log_{c} (x^{7})$ by moving $\frac{1}{6}$ inside the logarithm.

$\log_{c} ({(x^{7})}^{\frac{1}{6}}) - \log_{c} (y^{6} z^{5})$

Step 1.2

Multiply the exponents in ${(x^{7})}^{\frac{1}{6}}$ .

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Step 1.2.1

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

$\log_{c} (x^{7 (\frac{1}{6})}) - \log_{c} (y^{6} z^{5})$

Step 1.2.2

Combine $7$ and $\frac{1}{6}$ .

$\log_{c} (x^{\frac{7}{6}}) - \log_{c} (y^{6} z^{5})$

Step 2

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

$\log_{c} (\frac{x^{\frac{7}{6}}}{y^{6} z^{5}})$