Precalculus Examples

$\frac{1}{2} \cdot \log (x) + 4 \log (y)$

Step 1

Simplify each term.

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Step 1.1

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

$\log (x^{\frac{1}{2}}) + 4 \log (y)$

Step 1.2

Simplify $4 \log (y)$ by moving $4$ inside the logarithm.

$\log (x^{\frac{1}{2}}) + \log (y^{4})$

Step 2

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

$\log (x^{\frac{1}{2}} y^{4})$

Step 3

Reorder factors in $\log (x^{\frac{1}{2}} y^{4})$ .

$\log (y^{4} x^{\frac{1}{2}})$