# How do you solve for x in this radical equation?

1. Oct 23, 2005

### 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?

Last edited: Oct 24, 2005
2. Oct 24, 2005

### TD

You can use logarithms or 'play' with powers:

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

3. Oct 24, 2005

### HallsofIvy

Staff Emeritus
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
$$^2\sqrt{x}$$