Answer
$x=1$
Work Step by Step
$2^{x}-10(2^{-x})+3=0$
Rewrite the second term of this equation as $-\dfrac{10}{2^{x}}$:
$2^{x}-\dfrac{10}{2^{x}}+3=0$
Multiply the whole equation by $2^{x}$:
$2^{x}\Big(2^{x}-\dfrac{10}{2^{x}}+3=0\Big)$
$2^{2x}-10+3(2^{x})=0$
$2^{2x}+3(2^{x})-10=0$
Factor this equation:
$(2^{x}+5)(2^{x}-2)=0$
Set both factors equal to $0$ and solve each individual equation:
$2^{x}+5=0$
Take the $5$ to the right side:
$2^{x}=-5$
Since no value of $x$ makes this first equation true, it has no solution. Let's move on to the other one:
$2^{x}-2=0$
Take the $-2$ to the right side:
$2^{x}=2$
Simply use the one-to-one property to solve this equation:
$2^{x}=2$
$x=1$