# How do you express the sum or difference of logarithms?

Category:
science
physics

To write the

**sum or difference of logarithms**as a single**logarithm**, you will need to learn a few rules. The rules are ln AB = ln A + ln B. This is the addition rule. The multiplication rule of**logarithm**states that ln A/b = ln A - ln B.

Then, how do you find the sum of a log?

A useful property of **logarithms** states that the **logarithm** of a product of two quantities is the **sum** of the **logarithms** of the two factors. In symbols, logb(xy)=logb(x)+logb(y). ? ( x y ) = log b ? ( x ) + log b ?

**exponents**, these rules come from the rules of

**exponents**. Let a be greater than 0 and not equal to 1, and let n and m be real numbers.

In this manner, how do you express powers as a factor?

**write the expression as a single logarithm express powers as factors must show work**

- combine + terms with multiplication.
- cancel common factors.
- combine - terms with division.
- cancel common factors.
- write as negative exponent.
- use power rule.

Recall that we use the product rule of exponents to combine the product of exponents by adding: xaxb=xa+b x a x b = x a + b . We have a similar **property** for **logarithms**, called the product rule for **logarithms**, which says that the logarithm of a product is equal to a sum of **logarithms**.