Question

Evaluate the log without a calculator ( Show your work ) mula1" title="log_{81} 27" alt="log_{81} 27" align="absmiddle" class="latex-formula">

Answer 1

Answer:

3/4 ( or 0.75).

Step-by-step 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

Answer:

$\log_{81}(27)=\frac{3}{4}$

Step-by-step explanation:

The given logarithm is

$\log_{81}(27)$

Let us change to base 3.

$\log_{81}(27)=\frac{\log_3(27)}{\log_3(81)}$

$\log_{81}(27)=\frac{\log_3(3^3)}{\log_3(3^4)}$

$\log_{81}(27)=\frac{3\log_3(3)}{4\log_3(3)}$

$\log_{81}(27)=\frac{3(1)}{4(1)}$

$\log_{81}(27)=\frac{3}{4}$