Question

What is the value of log81 3? Show your work.

Answer 1

hope this will help :)

Answer 2

Answer: The value is
`(1)/(4).`

Step-by-step explanation: We are given to find the value of the following logarithmic expression.

`E=\log_(81)3.`

We will be using the following logarithmic properties:

`(i)~\log_ba=(\log a)/(\log b),\\\\(ii)~\log a^b=b\log a.`

The solution is as follows:

`E\\\\=\log_(81)3\\\\\\=(\log 3)/(\log 81)\\\\\\=(\log 3)/(\log 3^4)\\\\\\=(\log 3)/(4\log 3)\\\\\\=(1)/(4).`

Thus, the required value of the given expression is
`(1)/(4).`