Precalculus Examples

$3 \log (A) - 5 \log (B) + 2 \log (B)$

Step 1

Simplify each term.

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Step 1.1

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

$\log (A^{3}) - 5 \log (B) + 2 \log (B)$

Step 1.2

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

$\log (A^{3}) - \log (B^{5}) + 2 \log (B)$

Step 1.3

Simplify $2 \log (B)$ by moving $2$ inside the logarithm.

$\log (A^{3}) - \log (B^{5}) + \log (B^{2})$

Step 2

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

$\log (\frac{A^{3}}{B^{5}}) + \log (B^{2})$

Step 3

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

$\log (\frac{A^{3}}{B^{5}} B^{2})$

Step 4

Cancel the common factor of $B^{2}$ .

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Step 4.1

Factor $B^{2}$ out of $B^{5}$ .

$\log (\frac{A^{3}}{B^{2} B^{3}} B^{2})$

Step 4.2

Cancel the common factor.

$\log (\frac{A^{3}}{B^{2} B^{3}} B^{2})$

Step 4.3

Rewrite the expression.

$\log (\frac{A^{3}}{B^{3}})$