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Chapter 5: Q. 75 (page 284)

solve each equation. Verify your results using a graphing utility.
$4^{x} 2^{x^{2}} = 16^{2}$

Short Answer

Expert verified

The value of x for which the above equation is valid are :

$- 4, 2$

Step by step solution

01

Step 1. Given equation

$4^{x} 2^{x^{2}} = 16^{2}$

02

Step 2. Solving exponentially

$4^{x} 2^{x^{2}} = 16^{2} 2^{2 x} . 2^{x^{2}} = 2^{8} 2^{x^{2 + 2 x}} = 2^{8} \Rightarrow x^{2} + 2 x = 8 x^{2} + 2 x - 8 = 0 \Rightarrow x = - 4, 2$

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Most popular questions from this chapter

In Problems 61–72, the function f is one-to-one. Find its inverse and check your answer.

$f (x) = \frac{3 x + 4}{2 x - 3}$

The domain of a one-to-one functiong is $(- \infty, 0)$ , and its range is $[0, \infty)$ . State the domain and the range of $g^{- 1}$ .

If $f (x) = a^{x}$ , show that $\frac{f (x + h) - f (x)}{h} = a^{x} . \frac{a^{h} - 1}{h} h \neq 0$ .

Solve given equation and verify your result using graphing utility.

${(e^{4})}^{x} . e^{x}$ ²=e12

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

Solve:

$x^{2} + 3 x = 4$ x

See all solutions

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