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

1 Answer
Nov 17, 2016

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