Question

What is the value of x for x^(2/3) = 3? Can anyone show me the steps to solve this problem please?

Answer 1

Here is how I would solve this
\[x^{\frac{2}{3}}=3\]
Take log on both sides, bring down the exponent
\[\frac{2}{3}\log(x)=\log(3)\]
divide to isolate x
\[\log(x) = \frac{\log(3)\times3}{2}\]
raise both sides. 10 raised to log x is x.
\[x = 10^{\frac{\log
(3)\times3}{2}}\approx5.19615\]
I'm not sure if there is an easier way to do this.

Answer 2

Another way to do this is:

Since \[(x^{m})^{n} = x^{mn}\] then \[(x^{2 \over 3})^{3 \over 2} = x^{{2 \over 3} \times {3 \over 2}} = x^1 = x\]

So
\[ x^{2 \over 3} = 3\]
\[(x^{2 \over 3})^{3 \over 2} = 3^{3 \over 2}\]
\[x = (3^3)^{1 \over 2}=\sqrt {27} \approx 5.196\]

Answer 3

ahh - of course, and that is simpler.