Solve the equation for `x:` `2^(2x+1)=17. 2^x-2^3`

Explanation

`2^(2x+1)=17. 2^x-2^3`
`2^(2x+1)=(16+1)xx2^(x)-2^3`
Since,`2^4=16`
So,
`2^(2x+1)=(2^4+1)xx2^(x)-2^3`
`2^(2x+1)=2^4xx2^(x)+2^(x)-2^(3)`
`2^(2x+1)-2^x=2xx2^3xx2^(x)-2^(3)`
`2^(2x+1)-2^(x)=2^3\(x^(x+1)-1)`
`2^x\(x^(x+1)-1)=2^3\(x^(x+1)-1)`
`2^(x)=2^(3)`
We know that, if base are same the powers will be equal. So,
`x=3`
So, the value of `x` is `3`