Precalculus Examples

$\log_{a} (b c) - \log_{a} (\frac{c}{b})$

Step 1

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

$\log_{a} (\frac{b c}{\frac{c}{b}})$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\log_{a} (b c \frac{b}{c})$

Step 3

Cancel the common factor of $c$ .

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Step 3.1

Factor $c$ out of $b c$ .

$\log_{a} (c b \frac{b}{c})$

Step 3.2

Cancel the common factor.

$\log_{a} (c b \frac{b}{c})$

Step 3.3

Rewrite the expression.

$\log_{a} (b \cdot b)$

Step 4

Raise $b$ to the power of $1$ .

$\log_{a} (b^{1} b)$

Step 5

Raise $b$ to the power of $1$ .

$\log_{a} (b^{1} b^{1})$

Step 6

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\log_{a} (b^{1 + 1})$

Step 7

Add $1$ and $1$ .

$\log_{a} (b^{2})$