# How do you evaluate log_27 3?

Aug 28, 2016

${\log}_{27} 3 = \frac{1}{3}$

#### Explanation:

Try to read log expressions in this form as a question...

3 " is which power of " 27?

OR: "What index of 27 will give "3?

You should recognise that 3 is the cube root of 27

In index form this is: ${27}^{x} = 3$

root3 (27) = 3 " or 27^(1/3) = 3.

${\log}_{27} 3 = \frac{1}{3}$

In the same way try to answer these by inspection:

${\log}_{7} 49 , \text{ "log_5 125 , " " log_36 6 " } {\log}_{32} 2$

The answers in reverse order are:
$\frac{1}{5} , \text{ " 1/2" " 3, " } 2$