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

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.

$16 = {2}^{x} \cdot {2}^{1} - {2}^{x} = {2}^{x} \cdot 2 - {2}^{x}$

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

$16 = {2}^{x} \left(2 - 1\right) = {2}^{x}$

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 $x = 4$?