Question

How do you solve `27= x ^ { \frac { 3} { 2} }`?

Answer 1

`x=9`

Explanation:

`x^(3/2)=27`

Take `log_3` in both sides of the equation, you get

`log_3(x^(3/2))=log_3(27)`

Using the power property of logarithms `log_b(a^p)=p*log_b(a)`, expand the left hand side of the equation. Simplify the right hand side also to get

`3/2log_3(x)=3`

Multiply by `2/3` on both sides of the equation

`cancel(2/3)*cancel(3/2)log_3(x)=3*2/3 -> log_3(x)=2`

Convert `log_3(x)=2` to exponential form

`log_3(x)=2->3^2=x`

So `x=9` is your final answer