Question

Hello friends, please, I need to know how to get the answer out of this exponential equation? thank you

Answer 1

No real solutions

Explanation:

`2^(4 x) - 16^(x + 3) - 4^(x - 1) =0->4^(2x)-4^(2(x+3))-4^x/4=0` or
`4 cdot 4^(2x)-4^7cdot4^(2x)-4^x=0` or
`((4-4^7)4^x-1)4^x=0`

but `4^x ne 0` so

`(4-4^7)4^x-1=0` then

`4^x=-1/(4(4^6-1))`

but for `x in RR` we have `4^x > 0` so no real solutions