Chapter 5 - Exponential Functions - 5.2 Solving Equations Using Exponent Rules - 5.2 Exercises - Page 438: 79

$x \approx \pm2.59$

$5x^{6} - 30 = 1475$ $5x^{6} = 1475 + 30$ $5x^{6} = 1505$ $x^{6} = 301$ $x = \pm301^{\frac{1}{6}}$ $x = \pm2.589...$ $x \approx \pm2.59$ Check: $5x^{6} - 30 \overset{?}{=} 1475$ $5(\pm2.589...)^{6} - 30 \overset{?}{=} 1475$ $5(301) - 30 \overset{?}{=} 1475$ $1505 - 30 \overset{?}{=} 1475$ $1475 = 1475$