# How do you evaluate log_81 27?

Aug 3, 2016

${\log}_{81} 27 = \frac{3}{4}$

#### Explanation:

Using the change of base formula:

${\log}_{a} b = \frac{{\log}_{c} b}{{\log}_{c} a}$

and the definition of logarithm as the inverse of exponentiation:

${\log}_{a} {a}^{b} = b$

we find:

${\log}_{81} 27 = \frac{{\log}_{3} 27}{{\log}_{3} 81} = \frac{{\log}_{3} {3}^{3}}{{\log}_{3} {3}^{4}} = \frac{3}{4}$