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What is the exact value of : log (9) 81

| Certified Educator

Given the logarithm number log9 81

We need to determine the real value of the numbers.

We will use logarithm properties to simplify and calculate the values.

First we will rewrite 81 = 9^2

==> log9 81 = log9 9^2

Now we know from logarithm properties that log a^b = b*log a

==> log9 9^2 = 2*log9 9

==> log9 81 = 2*log9 9

Now we know that loga a = 1

==> log9 81 = 2*log9 9 = 2*1 = 2

Then the exact values of log9 81 = 2

Approved by eNotes Editorial

| Certified Educator

We need to find the value of log 81 where the base of the log is 9.

Now for a logarithm to any base log a^b = b*log a, and log(a) a = 1.

So log (9) 81

=> log (9) 9^2

=> 2* log (9) 9

=> 2* 1

=> 2

Therefore log (9) 81 = 2.

Approved by eNotes Editorial