How do you evaluate log_27 9?

1 Answer
Aug 7, 2016

x = 2/3

Explanation:

In log form the question being asked is ...

"To what power must 27 be raised to give 9?#

You should recognise 27 as 3^3 and 9 as 3^2

3 = root3(27) = 27^(1/3)

9 = 3^2 = (root3(27))^2 = 27^((1/3)^2) = 27^(2/3)

OR

log_27 9 = x rArr " " 27^x = 9

3^(3x) = 3^2

Equating exponents: 3x = 2

x = 2/3