# What are the three laws of logarithms?

*print*Print*list*Cite

### 2 Answers

Law 1:

log x + log y = log (x*y)

Example:

log 2 + log 5 = log (2*5) = log 10 = 1

Law 2:

log x - log y = log x/y

Example:

log 100 - log 10 = log 100/10 = log 10 = 1

Law 3:

log x^a = a* log x

Example:

log 100 = log 10^2 = 2*log 10 = 2*1 = 2

There are many laws of logarithms, I do not know which three you are referring you.

Here are a few laws that are commonly used:

log(a*b) = log a + log b, used while multiplying numbers

log(a/b) = log a - log b, used while dividing numbers

log(a^n) = n*log a, used to find the power of a number

log(a) b = [log(c) b] / [log(c) a], used to change the base of the log from a to c

log(b) a = 1/ log(a) b

log(a) a = 1