Algebra involves Logarithms and exponents. Logarithms were developed for making complicated calculations simple. However, with the advent of computers and hand calculators, doing calculations with the use of logarithms is no longer necessary. But still, logarithmic and exponential equations and functions are commonly used in mathematics. A logarithmic function is the inverse of an exponential function. An exponential function is the inverse of a logarithmic function. Therefore, the two types of functions are related and either can be rewritten in the form of the other.
Take an exponential equation an =b this can be written as
loga b = n.
There are some basic laws for solving logarithmic and exponential functions.
The following examples explain the use of logarithmic functions on solving.
Example 1:- Solve for x. logx 243 = -5
Solution 1:- We need to change this into exponential form
x- 5 = 243
x-5= 35 (because 243 = 35 )
(1/ x) 5 = 35 (because a –n = (1/ a) n)
1/x = 3
x = 1/3 is the required solution
Example 2:- Evaluate the following
log672 – log6 2
Solution 2:- log672 – log6 2
log6 72 /2 =log6 36 = log6 62(by using quotient law)
= 2 log6 6
= 2. 1 (because loga a = 1)
Therefore after evaluation, we find that the value of log672 – log6 2 is coming out to be 2.