Question

What is the value of log27 9?

Answer 1

the value of log_27 9 is 2/3

Answer 2

2/3

Explanation:

`log_(27)(9)`

WE have base 27

LEts apply change of base formula

`log_b(a)=(log a)/(log b)`

`log_(27)(9)=(log 9)/(log 27)`

Now we write 27 and 9 in exponential form

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

Use power property and move the exponent before log

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

canel out log 3 at the top and bottom

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