Precalculus Examples

$\frac{1}{2} \cdot (\log_{b} (M) + \log_{b} (N) - \log_{b} (P))$

Step 1

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

$\frac{1}{2} \cdot (\log_{b} (M N) - \log_{b} (P))$

Step 2

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

$\frac{1}{2} \cdot \log_{b} (\frac{M N}{P})$

Step 3

Simplify $\frac{1}{2} \log_{b} (\frac{M N}{P})$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{b} ({(\frac{M N}{P})}^{\frac{1}{2}})$

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 4.1

Apply the product rule to $\frac{M N}{P}$ .

$\log_{b} (\frac{{(M N)}^{\frac{1}{2}}}{P^{\frac{1}{2}}})$

Step 4.2

Apply the product rule to $M N$ .

$\log_{b} (\frac{M^{\frac{1}{2}} N^{\frac{1}{2}}}{P^{\frac{1}{2}}})$