Question

Find the value of x if nine and one half times nine and one half equals x to the root of 81

Answer 1

x=2

Explanation:

Based on your description I am assuming your equation is:

`{9}^{ (1)/(2) } * {9}^{ (1)/(2) } = \sqrt[x]{81}`

To find x in the above equation, we need to simplify the LHS

`√(9) * √(9) = \sqrt[x]{81}`

Combine the roots on the LHS

`√(9 * 9) = \sqrt[x]{81}`

We simplify further to get;

`√(81) = \sqrt[x]{81}`

We can rewrite as

`{81}^{ (1)/(2) } = {81}^{ (1)/(x) }`

By equating exponents we get:

`(1)/(2) = (1)/(x)`

This implies that:

`x = 2`