Question

What is the value of log27 9?

Answer 1

the value of log_27 9 is 2/3

Answer 2

Answer:

2/3

Step-by-step explanation:

$log_{27}(9)$

WE have base 27

LEts apply change of base formula

$log_b(a)=\frac{log a}{log b}$

$log_{27}(9)=\frac{log 9}{log 27}$

Now we write 27 and 9 in exponential form

$log_{27}(9)=\frac{log 3^2}{log 3^3}$

Use power property and move the exponent before log

$log_{27}(9)=\frac{2log 3}{3log 3}$

canel out log 3 at the top and bottom

$log_{27}(9)=\frac{2}{3}$