Solve `x^(log_(4) x)=2^(3(log_(4)x+3)`.

Answer

` x = 64, 1/8`

Explanation

`x^(log_(4)x)=2^(3(log_(4)x+3)`
Taking log on both sides to the base 2, we get
`(log_(4)x)(log_(2)x) = (log_(4) x+3) log_(2) 8`
Putting ` log_(2) x = t`, we get
` 1/2 t^(2)(1/2t+3) 3`
` or t^(2) = 3t + 18`
` or t = 6, -3`
` or x = 2^(6), 2^(-3)`
` or x = 64, 1//8`