Give the Definition of Logarithms ?

A logarithm to the base a of a number x is the power to which a is raised to get x.

In equation format:

If x = ay, then log_a x = y.

Example 1: Convert the logarithmic equation log₃ 9 = 2 to an exponential equation.
Solution:
log₃ 9 = 2          3² = 9 By the definition of logarithms.
Example 2: Convert the logarithmic equation log₂ 16 = 4 to an exponential equation.
Solution:
log₂ 16 = 4         2⁴ = 16 By the definition of logarithms.
Example 3: Convert the logarithmic equation log₅ 1/25 = -2 to an exponential equation.
Solution:
log ₅ 1/25 = -2   5^-2 = 1/25 By the definition of logarithms.