Chapter 5 - Exponential Functions - 5.2 Solving Equations Using Exponent Rules - 5.2 Exercises - Page 438: 85

$b = \pm6$

$\frac{7b^{4}+58}{8} = 1141.25$ $7b^{4} + 58 = 9130$ $7b^{4} = 9130 - 58$ $7b^{4} = 9072$ $b^{4} = 1296$ $b = \pm1296^{\frac{1}{4}}$ $b = \pm6$ Check: $\frac{7b^{4}+58}{8} \overset{?}{=} 1141.25$ $\frac{7(\pm6)^{4}+58}{8} \overset{?}{=} 1141.25$ $\frac{7(1296)+58}{8} \overset{?}{=} 1141.25$ $\frac{9072+58}{8} \overset{?}{=} 1141.25$ $\frac{9130}{8} \overset{?}{=} 1141.25$ $1141.25 = 1141.25$