Find the values of `x` in each of the following : (i)`2^(5x)-:2^x=(root(5)2)^(20)` (ii)`(2^3)^4=(2^2)^x`

Explanation

(i)`2^(5x)-:2^x=(root(5)2)^(20)`
`2^(5x)/2^x=(2^20)^(1/5)`
`2^(5x−x)=2^(20/5)`
`2^(4x)=2^(20/5)`
On comparing the both sides, we get:
`4x=20/5`
`x=20/(5×4)=1`
`x=1`

(ii)`(2^3)^4=(2^2)^x`
`2^(3times4)=2^2x`
`2^12=2^2x`
On comparing the both sides, we get:
`2x=12`
`x=12/2=6`
`x=6`