Precalculus Examples

$\log (4) - \log (3) + \log (p) + 3 \log (r)$

Step 1

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

$\log (\frac{4}{3}) + \log (p) + 3 \log (r)$

Step 2

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

$\log (\frac{4}{3} p) + 3 \log (r)$

Step 3

Simplify each term.

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Step 3.1

Combine $\frac{4}{3}$ and $p$ .

$\log (\frac{4 p}{3}) + 3 \log (r)$

Step 3.2

Simplify $3 \log (r)$ by moving $3$ inside the logarithm.

$\log (\frac{4 p}{3}) + \log (r^{3})$

Step 4

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

$\log (\frac{4 p}{3} r^{3})$

Step 5

Combine $\frac{4 p}{3}$ and $r^{3}$ .

$\log (\frac{4 p r^{3}}{3})$