How do you evaluate log_81 3?

2 Answers
Shell
Nov 2, 2016

log_81 3 = 1/4

Explanation:

log_81 3 =x

Rewrite as an exponential. Remember, the answer to a log is the exponent. In this case x is the exponent, and 81 is the base.

81^x =3

Find a common base for both sides, which is 3.
81=3^4, so by substitution...

(3^4)^x=3

Use the exponent rule (x^a)^b=x^(ab)

3^(4x)=3^1

4x=1

x=1/4

Monzur R.
Nov 2, 2016

log_81(3)=1/4

Explanation:

Since 81 is much larger than 3, our answer will be a decimal, so let's think of this problem in the opposite sense: log_3(81). 3^4 = 81, so log_3(81) = 4.

Using the law of exponents, we know that if a^m = n, then n^(1/m) = a. So using this rule, we know that 81^(1/4) = 3, so log_81(3)=1/4

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