Chapter 5 - Exponential Functions - 5.2 Solving Equations Using Exponent Rules - 5.2 Exercises - Page 438: 82

$x \approx \pm1.75$

$74 - 3x^{12} = -2457$ $-3x^{12} = -2457 - 74$ $-3x^{12} = -2531$ $x^{12} = \frac{2531}{3}$ $x = \pm(\frac{2531}{3})^{\frac{1}{12}}$ by GDC / calculator $x = \pm1.7532...$ $x \approx \pm1.75$ Check: $74 - 3x^{12} \overset{?}{=} -2457$ $74 - 3(\pm1.7532...)^{12} \overset{?}{=} -2457$ $74 - 3(843.666...) \overset{?}{=} -2457$ $74 - 2531 \overset{?}{=} -2457$ $-2457 = -2457$