Logsssss!

The logarithmic function logb^x and the exponential function bx are inverse of each other, so that means

y = logb^x is equivalent to x = b^y

where b is the common base of the exponential and the logarithm.

The forms above helps in solving logarithmic and exponential functions and needs a deep understanding. Examples, of how the above relationship between the logarithm and exponential may be used to transform expressions, are presented below.

Example 1 : Change each logarithmic expression to an exponential expression.

1. log3^27 = 3

2. log36^6 = 1 / 2

3. log2^(1 / 8) = -3

4. log8^2 = 1 / 3

Solution to Example 1:

1. The logarithmic form log3^27 = 3 is equivalent to the exponential form

27 = 33


2. The logarithmic form log36^6 = 1 / 2 is equivalent to the exponential form
6 = 361/2


3. log2^(1 / 8) = -3 in exponential form is given by

1 / 8 = 2-3


4. log8^2 = 1 / 3 in exponential form is given by

2 = 81/3