# How do you solve #2x^(3/4)=54#?

##### 1 Answer

Jul 31, 2016

#### Explanation:

Divide both sides by

#x^(3/4) = 27 = 3^3#

If

#x = x^1 = x^(3/4*4/3) = (x^(3/4))^(4/3) = (3^3)^(4/3) = 3^(3*4/3) = 3^4 = 81#

**Other solutions?**

Are there any negative or Complex solutions?

Suppose

Then:

#x^(3/4) = r^(3/4)(cos ((3theta)/4) + i sin ((3 theta)/4))#

For the imaginary part to be

So

This can only lie in the range

So the only solution is the one on the positive part of the Real axis, i.e.