Precalculus Examples

$\frac{1}{2} \cdot \log (x) - \log (y) + \log (3 z)$

Step 1

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

$\log (x^{\frac{1}{2}}) - \log (y) + \log (3 z)$

Step 2

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

$\log (\frac{x^{\frac{1}{2}}}{y}) + \log (3 z)$

Step 3

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

$\log (\frac{x^{\frac{1}{2}}}{y} (3 z))$

Step 4

Rewrite using the commutative property of multiplication.

$\log (3 \frac{x^{\frac{1}{2}}}{y} z)$

Step 5

Combine $3$ and $\frac{x^{\frac{1}{2}}}{y}$ .

$\log (\frac{3 x^{\frac{1}{2}}}{y} z)$

Step 6

Combine $\frac{3 x^{\frac{1}{2}}}{y}$ and $z$ .

$\log (\frac{3 x^{\frac{1}{2}} z}{y})$

Step 7

Reorder factors in $\log (\frac{3 x^{\frac{1}{2}} z}{y})$ .

$\log (\frac{3 z x^{\frac{1}{2}}}{y})$