Example   Evaluate log₅ 7 .

Solution

At first, notice that we can't employ the similar method to do this evaluation which we did in the first set of instance. It would need us to look at the following exponential form,

                                                           5^?  = 7

and that's only not something which anyone can answer off the top of their head.  If the 7 had been a 5, or a 25, or a 125, etc. we could do this, however it's not. Thus, we need to use the change of base formula.

Now, we can utilize either one & we'll get the similar answer.  Thus, let's use both & verify that. We'll begin with the common logarithm through of the change of base.

log₅  7 = log 7/ log 5 = 0.845098040014/0.698970004336 = 1.20906195512

Now, let's attempt the natural logarithm form of the change of base formula.

log₅  7 = log 7/ log 5 = 1.94591014906 /0.698970004336 = 1.20906195512

So, we got the same answer despite the fact that the fractions involved different answers.