# Chapter 2 - Nonlinear Functions - 2.4 Exponential Functions - 2.4 Exercises - Page 86: 26

$$8^{ x^{2} }=2^{x+4}$$ The solution of the given equation is $$x=\frac{4}{3} \quad \text { or } \quad x=-1.$$

#### Work Step by Step

$$8^{ x^{2} }=2^{x+4}$$ Since the bases must be the same, write 8 as $2^{3 }$ giving \begin{aligned} 8^{ x^{2} }&=2^{x+4} \\\left(2^{3}\right)^{x^{2}} &=2^{x+4} \\ 2^{3 x^{2}} &=2^{x+4} \\ 3 x^{2} &=x+4 \\ 3 x^{2} &-x-4=0 \\(3 x-4)(x+1) &=0 \\ x=\frac{4}{3} & \text { or } \quad x=-1 \end{aligned} So, the solution of the given equation is $$x=\frac{4}{3} \quad \text { or } \quad x=-1.$$

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