A logarithm is an exponent. Logarithm is an opposite of exponential. You may
consider logarithms as being inverse of exponential.
If : y = b
x is called the logarithm of y with base b.
It is written as: logby = x
For example: 8 = 2 3 . So 3 is called the logarithm of 8 with base 2.
So: log 2 = 3
The logarithm of a positive number, y, with a positive base, b (b ≠1), is defined as
the exponent or the power to which the base b is raised to produce the number y.
Example: 10000 = 10 4
So log100000 = 4
The logarithm of 10000 with base 10 is 4.
10 is the exponent to which 10 (the base) must be raised to produce 10000.
10 4 = 10000 10 =10000 is called the exponential form
log100000 = 4 is called the logarithm form
So: log b = x means that y = b x
logby = x ⇔ y = b x
Take: b = 10 ⇒ log10y = x ⇔ y = 10 x
log bmn) = log m + bog n b (Addition)
log ( ) = log m − log n
b n b b (Subtraction)
log (m ) = nlog m (Power)
b b Example:
A = (3)×(4) ⇒