Question

How do you solve `2^x=4^(x+1)`?

Answer 1

Re-express the right hand side as `2^(2x+2)` to find `x = -2`

Explanation:

`(a^b)^c = a^(bc)` and `4 = 2^2`, so...

`2^x = 4^(x+1) = (2^2)^(x+1) = 2^(2(x+1)) = 2^(2x+2)`

So `x = 2x+2`

Subtract `(x + 2)` from both sides to get `x = -2`