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

1 Answer
May 9, 2018

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?