Question

Which of the following is equivalent to log27 9?

answer choices:
a 1/3
b 2/3
c 3/2
d 0.798

Answer 1

The corect answer is b) 2/3 because 27^(2/3) = (3^3)^(2/3) = 3^[ 3 x (2/3) ] = 3^(6/3) = 3^2 = 9;

Answer 2

option B : 2/3

Explanation:

log_27(9)

base of log is 27

We try to write 9 in exponential form with base 27

9 can be written as 3^2

27 can be written as 3^3

To need to get base 27

`27^{(2)/(3)}=(3^3)^{(2)/(3)}= 3^{(6)/(3)} = 3^2 = 9`

So 9 can be written as 27^2/3

`log_(27)(9)=log_(27)(27^{(2)/(3)})`

Apply log property and move exponent 2/3 before log

`log_(27)(9)=(2)/(3)log_(27)(27)`

log_27(27) is 1

So answer is 2/3