Answer
1. Exponential equation
2. $x = -4$
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
$7(\frac{1}{3})^{x} + 142 = 2(\frac{1}{3})^{x} + 547$
$7(\frac{1}{3})^{x} - 2(\frac{1}{3})^{x} = 547 - 142$
$(7-2)(\frac{1}{3})^{x} = 405$
$5(\frac{1}{3})^{x} = 405$
$(\frac{1}{3})^{x} = 81$
$3^{-x} = 81$
$3^{-x} = 3^{4}$
$-x = 4$
$x = -4$
Check:
$7(\frac{1}{3})^{-4} + 142 \overset{?}{=} 2(\frac{1}{3})^{-4} + 547$
$7(81) + 142 \overset{?}{=} 2(81) + 547$
$567 + 142 \overset{?}{=} 162 + 547$
$709 = 709$
