Question

(x2/5)n

For what value of n, written as a decimal, will the expression equal x?

Answer 1

Given:

The expression is:

`\left(x^{(2)/(5)\right)^n`

To find:

The decimal value of n so that the value of the given expression is equal to x.

Solution:

We have,

`\left(x^{(2)/(5)\right)^n`

This expression is equal to x.

`\left(x^{(2)/(5)\right)^n=x`

`x^{(2)/(5)n}=x^1`
`[\because (a^m)^n=a^(mn)]`

On comparing the exponents, we get

`(2)/(5)n=1`

`2n=5`

`n=(5)/(2)`

`n=2.5`

Therefore, the required value of n is 2.5.