Precalculus Examples

$x \log_{2} (m) + \frac{1}{y} \cdot \log_{2} (n) - \log_{2} (p)$

Step 1

Combine $\frac{1}{y}$ and $\log_{2} (n)$ .

$x \log_{2} (m) + \frac{\log_{2} (n)}{y} - \log_{2} (p)$

Step 2

To write $x \log_{2} (m)$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{x \log_{2} (m) y}{y} + \frac{\log_{2} (n)}{y} - \log_{2} (p)$

Step 3

Combine the numerators over the common denominator.

$\frac{x \log_{2} (m) y + \log_{2} (n)}{y} - \log_{2} (p)$

Step 4

To write $- \log_{2} (p)$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{x \log_{2} (m) y + \log_{2} (n)}{y} - \log_{2} (p) \cdot \frac{y}{y}$

Step 5

Combine $- \log_{2} (p)$ and $\frac{y}{y}$ .

$\frac{x \log_{2} (m) y + \log_{2} (n)}{y} + \frac{- \log_{2} (p) y}{y}$

Step 6

Combine the numerators over the common denominator.

$\frac{x \log_{2} (m) y + \log_{2} (n) - \log_{2} (p) y}{y}$

Step 7

Reorder factors in $\frac{x \log_{2} (m) y + \log_{2} (n) - \log_{2} (p) y}{y}$ .

$\frac{x y \log_{2} (m) + \log_{2} (n) - y \log_{2} (p)}{y}$