Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

Simplify $- 5 \log_{2} (b)$ by moving $5$ inside the logarithm.

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

Step 1.2

Simplify $3 \log_{2} (c)$ by moving $3$ inside the logarithm.

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

Step 2

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

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

Step 3

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

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

Step 4

Combine $\frac{a}{b^{5}}$ and $c^{3}$ .

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