Rules of Logarithms

In this section let me help you go through logarithm rules

Definition on Logarithm:-

The logarithm of a number is the exponent to which a base must be raised to equal that number. For example if 5³ = 125, it is said that log₅ 125= 3. Or, in general , if a³ = m, then log_a m =3 . where ‘a’ is called the base of logarithm. Evidently ‘a’ cannot be 1 ( ≠1).

The rules of logarithms are as follows:

Log_a mn = log_a m + log_an, where ‘a’ is any positive number such that a≠1

Log_a m/n= log_a m - log_an , and

Log_a m^b = b log_a m

Where b is any rational number and m and n are positive number.You can apply the same rules on corresponding angles

Example Log15 = Log 5 + Log 3

Log 4/5= Log 4 – Log 5

Log64= Log 4³ = 3 Log 4

Exercise1. convert into exponential form log_m n = p

Options A. n^p = m

B. m^p= n

C. p^m= n

D mⁿ=p

Correct answer B