# Chapter 5 - Exponential Functions - 5.2 Solving Equations Using Exponent Rules - 5.2 Exercises: 100

$x \approx ±6$

#### Work Step by Step

1. Power 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 $\frac{1}{3}x^{8} - 24 = \frac{5}{3}x^{8} - 2239464$ $\frac{x^{8}}{3} - \frac{5x^{8}}{3} = -2239464 + 24$ $-\frac{4x^{8}}{3} = -2239440$ $\frac{4x^{8}}{3} = 2239440$ $4x^{8} = 6718320$ $x^{8} = 1679580$ $x = ±(1679580)^{\frac{1}{8}}$ $x = ±5.999...$ $x \approx ±6$ Check: When $x = 6$ $\frac{1}{3}(5.99...)^{8} - 24 \overset{?}{=} \frac{5}{3}(5.99...)^{8} - 2239464$ $\frac{1}{3}(1679580.001) - 24 \overset{?}{=} \frac{5}{3}(1679580.001) - 2239464$ $\frac{1679580.001}{3}- 24 \overset{?}{=} \frac{5(1679580.001)}{3} - 2239464$ $559860.003- 24 \overset{?}{=} 2799300.002 - 2239464$ $559836.003 \approx 559836.0017$ $559,836 \approx 559,836$ When $x = -6$ $\frac{1}{3}(-5.99...)^{8} - 24 \overset{?}{=} \frac{5}{3}(-5.99...)^{8} - 2239464$ $\frac{1}{3}(1679580.001) - 24 \overset{?}{=} \frac{5}{3}(1679580.001) - 2239464$ $\frac{1679580.001}{3}- 24 \overset{?}{=} \frac{5(1679580.001)}{3} - 2239464$ $559860.003- 24 \overset{?}{=} 2799300.002 - 2239464$ $559836.003 \approx 559836.0017$ $559,836 \approx 559,836$

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