# Question #7f1e9

Jan 19, 2018

$\log \left(y \times \frac{7 x}{5}\right) = \log \left(y\right) + \log \left(7\right) + \log \left(x\right) - \log \left(5\right)$

#### Explanation:

Logarithmic functions are a way of 'linearizing' higher-order functions like multiplication and division. Multiplication becomes 'addition' and division becomes 'subtraction' when in logarithmic form.

$\log \left(y \times \frac{7 x}{5}\right)$ can be separated into separate log functions added together.
$\log \left(y \times \frac{7 x}{5}\right) = \log \left(y\right) + \log \left(7 x\right) - \log \left(5\right)$ or even further:

$\log \left(y \times \frac{7 x}{5}\right) = \log \left(y\right) + \log \left(7\right) + \log \left(x\right) - \log \left(5\right)$