Question

How to solve `16 + 2^x = 2^(x+1)` without calculator?

Answer 1

`x=4`

Explanation:

Let's do our best to isolate `x` because that is what we are solving for. First subtract `2^x` from both sides of the equation.

`16=2^(x+1)-2^x`

Now use the properties of exponents to rewrite the right-hand side of the equation.

`16=2^x*2^1-2^x=2^x*2-2^x`

Now factor out `2^x` from the right-hand side of this equation.

`16=2^x(2-1)=2^x`

If you can't see that `x=4` from this equation rewrite `16` as `2^4`.

`2^4=2^x`

Now do you see that `x=4`?