Precalculus Examples

$\log_{b} (2 y + 5) - \frac{1}{2} \cdot \log_{b} (y + 3)$

Step 1

Multiply $- \frac{1}{2} \log_{b} (y + 3)$ .

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Step 1.1

Reorder $\log_{b} (y + 3)$ and $\frac{1}{2}$ .

$\log_{b} (2 y + 5) - (\frac{1}{2} \log_{b} (y + 3))$

Step 1.2

Simplify $\frac{1}{2} \log_{b} (y + 3)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{b} (2 y + 5) - \log_{b} ({(y + 3)}^{\frac{1}{2}})$

Step 2

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

$\log_{b} (\frac{2 y + 5}{{(y + 3)}^{\frac{1}{2}}})$