Wed February 23, 2011 By: Rishita Gajbhiye

what is logarithm,can you pls tell me all the formulaes and rules of it?

Expert Reply
Wed February 23, 2011

Dear Student,

A logarithm is just an exponent.

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 = by, then we say that y is “the logarithm of x to the base b” or “the base-b logarithm of x”. In symbols, y = logb(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 logbx function is defined as the inverse of the bx function. These two statements express that inverse relationship, showing how an exponential equation is equivalent to a logarithmic equation:

x = by       is the same as       y = logbx







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