Check out some similar questions!

ashwinmo · May 12, 2013, 11:34 PM

(3x-1)^2/3=3/4
how do I find x?

ebaines · May 13, 2013, 06:11 AM

Starting with:

$ (3x-1)^{2/3}=\frac 3 4 $

You can raise both sides to a factor of 1 over the (2/3) power, which is 3/2:

$ [(3x-1)^{2/3}]^{3/2}=(\frac 3 4)^{(3/2)} $

Why do we do this trick? Recall that when raising a number $w^a$ to the b power you get $(w^a)^b = w^{ab}$ . If b is the inverse of a then you have $(w^a)^{1/a} = w^1 = w$ . So raising both sides to the power of 1/a gets rid of the exponent on the left hand side. Applying this technique to your equation, where a = 2/3, turns the left hand side into:

$ [(3x-1)^{2/3}]^{3/2}=(3x-1)^{\frac 2 3 \times \frac 3 2 } = (3x-1)^1 = 3x-1 $

Can you take it from here?