Precalculus Examples

$3 \log (2) - \frac{1}{2} \cdot \log_{x} (3 - x)$

Step 1

Simplify $3 \log (2)$ by moving $3$ inside the logarithm.

$\log (2^{3}) - \frac{1}{2} \cdot \log_{x} (3 - x)$

Step 2

Raise $2$ to the power of $3$ .

$\log (8) - \frac{1}{2} \cdot \log_{x} (3 - x)$

Step 3

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

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Step 3.1

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

$\log (8) - (\frac{1}{2} \log_{x} (3 - x))$

Step 3.2

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

$\log (8) - \log_{x} ({(3 - x)}^{\frac{1}{2}})$