Since logarithmic functions are the inverse of an exponential functions, they must follow the laws of exponents. The three properties of logs listed below will be used to combine and solve expressions and equations in this section and the next. Each of these properties are derived from the laws of exponents.
| Log of a Product | $$\log_a (xy) = \log_a (x) + \log_a (y)$$ |
| Log of a Quotient | $$\log_a \frac{x}{y} = \log_a x – \log_a y$$ |
| Log of a Power |
We’ll being our focus with first of three properties: log of a product.
$\log 7x$ → For this, notice that 7 and ‘x’ are products; hence, they can be written separately as the sum of two logs → log 7 + log x
log 3 + log x + log y → Notice that there are three terms all containing log of base 10. This means we can write 3, x, and y as products under one log → log 3xy
The next few examples pertain to the We’ll being our focus with first of three properties: log of a product.