Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

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

$\log (2^{2}) x + 2 \log (2) y - \frac{1}{2} \cdot (\log (2) z)$

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

Multiply $- \frac{1}{2} (\log (2) z)$ .

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Step 1.5.1

Reorder $\log (2)$ and $\frac{1}{2}$ .

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

Step 1.5.2

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

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

Step 2

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

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