Precalculus Examples

$\frac{1}{2} \cdot \log_{2} (x) + 4 \log_{2} (w) - \log_{2} (y)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

$\log_{2} (x^{\frac{1}{2}}) + 4 \log_{2} (w) - \log_{2} (y)$

Step 1.2

Simplify $4 \log_{2} (w)$ by moving $4$ inside the logarithm.

$\log_{2} (x^{\frac{1}{2}}) + \log_{2} (w^{4}) - \log_{2} (y)$

Step 2

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

$\log_{2} (x^{\frac{1}{2}} w^{4}) - \log_{2} (y)$

Step 3

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

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

Step 4

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

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