How do you evaluate $log_27 9$ ?

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Answer 1 · 2016-08-07T18:16:41

$x = 2/3$

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: $3x = 2$

$x = 2/3$

How do you evaluate log_27 9log_27 9?