CBSE Class 11-science Answered

Dear Student,

To be specific, the logarithm of a number x to a base b is just the exponent you put onto b to make the result equal x. For instance, since 5² = 25, we know that 2 (the power) is the logarithm of 25 to base 5. Symbolically, log₅(25) = 2.

More generically, if x = b^y, then we say that y is “the logarithm of x to the base b” or “the base-b logarithm of x”. In symbols, y = log_b(x). Every exponential equation can be rewritten as a logarithmic equation, and vice versa, just by interchanging the x and y in this way.

Another way to look at it is that the log_bx function is defined as the inverse of the b^x function. These two statements express that inverse relationship, showing how an exponential equation is equivalent to a logarithmic equation:

x = b^y       is the same as       y = log_bx