How do you solve for x in this radical equation?

[Quasaire]

sqrt[x]{64} = 4

How do you solve for x?

I mean obviously the answer is x = 3 but how do you prove this algebraically?

 

[TD]

You can use logarithms or 'play' with powers:

\sqrt[x]{{64}} = 4 \Leftrightarrow 64^{1/x} = 4 \Leftrightarrow \left( {4^3 } \right)^{1/x} = 4 \Leftrightarrow 4^{3/x} = 4^1 \Leftrightarrow \frac{3}<br /> {x} = 1

 

[HallsofIvy]

I really, really wish people would say "x-root" rather than "x-square root" or root[x} instead of (as here) sqrt[x]. "square root" means specifically
^2\sqrt{x}