Precalculus Examples

$\log_{3} (4) - \frac{1}{2} \cdot \log_{3} (6 x - 5)$

Step 1

Multiply $- \frac{1}{2} \log_{3} (6 x - 5)$ .

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Step 1.1

Reorder $\log_{3} (6 x - 5)$ and $\frac{1}{2}$ .

$\log_{3} (4) - (\frac{1}{2} \log_{3} (6 x - 5))$

Step 1.2

Simplify $\frac{1}{2} \log_{3} (6 x - 5)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{3} (4) - \log_{3} ({(6 x - 5)}^{\frac{1}{2}})$

Step 2

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

$\log_{3} (\frac{4}{{(6 x - 5)}^{\frac{1}{2}}})$