Question

Evaluate the log without a calculator ( Show your work )


`log_(81) 27`

Answer 1

3/4 ( or 0.75).

Explanation:

let y = log81 27, then:

27 = 81^y ( by the definition of a logarithm).

27 = 3^3 and 81 = 3^4

So 27 = 81 ^3/4

so y = log81 27 = = 3/4.

Answer 2

`\log_(81)(27)=(3)/(4)`

Explanation:

The given logarithm is

`\log_(81)(27)`

Let us change to base 3.

`\log_(81)(27)=(\log_3(27))/(\log_3(81))`

`\log_(81)(27)=(\log_3(3^3))/(\log_3(3^4))`

`\log_(81)(27)=(3\log_3(3))/(4\log_3(3))`

`\log_(81)(27)=(3(1))/(4(1))`

`\log_(81)(27)=(3)/(4)`