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

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Answer 1 · 2018-05-09T00:02:16

$x = 4$ $x=4$

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

$16 = 2^{x + 1} - 2^{x}$ $16=2^(x+1)-2^x$

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

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

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

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

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

$2^{4} = 2^{x}$ $2^4=2^x$

Now do you see that $x = 4$ $x=4$ ?

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