Precalculus Examples

$\frac{1}{3} \cdot (\log_{2} (a^{5})) - \log_{2} (b c^{3})$

Step 1

Simplify each term.

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Step 1.1

Simplify $\frac{1}{3} (\log_{2} (a^{5}))$ by moving $\frac{1}{3}$ inside the logarithm.

$\log_{2} ({(a^{5})}^{\frac{1}{3}}) - \log_{2} (b c^{3})$

Step 1.2

Multiply the exponents in ${(a^{5})}^{\frac{1}{3}}$ .

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Step 1.2.1

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

$\log_{2} (a^{5 (\frac{1}{3})}) - \log_{2} (b c^{3})$

Step 1.2.2

Combine $5$ and $\frac{1}{3}$ .

$\log_{2} (a^{\frac{5}{3}}) - \log_{2} (b c^{3})$

Step 2

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

$\log_{2} (\frac{a^{\frac{5}{3}}}{b c^{3}})$