Answer
1. Exponential equation
2. $x = 7$
Work Step by Step
1. Exponential equation
For example:
$7^{x} + 3 = 0$ is an exponential equation. (The variable is the exponent.)
$x^{7} + 3 =0 $ is a power equation. (The variable is raised to the power of a number.)
2. Solve
$5(\frac{1}{2})^{x} - \frac{2}{32} = 3(\frac{1}{2})^{x} - \frac {3}{64}$
$5(\frac{1}{2})^{x} - 3(\frac{1}{2})^{x} = \frac{2}{32} - \frac{3}{64}$
$(5-3)((\frac{1}{2})^{x}) = \frac{1}{64}$
$2((\frac{1}{2})^{x}) = \frac{1}{64}$
$(\frac{1}{2})^{x} = \frac{1}{128}$
$2^{-x} = 128^{-x}$
$2^{-x} = 2^{-7}$
$-x = -7$
$x = 7$
Check:
$5(\frac{1}{2})^{7} - \frac{2}{32} \overset{?}{=}
3(\frac{1}{2})^{7} - \frac {3}{64}$
$5(\frac{1}{128}) - \frac{2}{32} \overset{?}{=}
3(\frac{1}{128}) - \frac {3}{64}$
$(\frac{5}{128}) - \frac{2}{32} \overset{?}{=}
(\frac{3}{128}) - \frac {3}{64}$
$-\frac{3}{128} = -\frac{3}{128}$
