# Logarithm Formulas

### Logarithm Formulas

[ ‘a > 0’, ‘b > 0’ and ‘m ∈ N’ ]

1. If

**a**^{m }**= b**, then we can write it as ‘**logₐb = m**‘ (read it as ‘**‘)***the value of logarithm of b with respect to base a is m*2. If logₐb = m , then we can write it as

**a**^{m }**= b**3. log (a × b) = log(a) + log(b)

4. log (a ÷ b) = log(a) – log(b)

5. log(a

^{m})^{ }= mlog(a)6. log(1) = 0

7. log

_{a}b = log(b)/log(a) = 1/log_{b}a8. a

^{loga}^{b}= b9. log(1/a) = – log(a)

10. log

_{a}a = 1^{ }

^{Note: If base of the logarithm is the number 10 then it is called “Basic/Common Logarithm” and if base of the logarithm is the number e (≈2.718) ,then it is called “Natural Logarithm“}