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Chapter 5: Q. 83 (page 284)

If $3^{- x} = 2$ , what does $3^{2 x}$ equal ?

Short Answer

Expert verified

The vale of $3^{2 x}$ is $\frac{1}{4}$

Step by step solution

01

Step 1. Given Information

Given :

$3^{- x} = 2$

We have to find $3^{2 x}$ .

02

Step 2. Write expression to be found in terms of given expression.

$3^{2 x} = {(3^{x})}^{2} = {(3^{- x})}^{- 2}$

03

Step 3. Put the given value in the expression and solve.

${(3^{- x})}^{- 2} = {(2)}^{- 2} = \frac{1}{2}$ ²=14

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Most popular questions from this chapter

The domain of one to one function g is $[0, 15]$ ,and its range is $(0, 8)$ . State the domain and range of $g^{- 1}$

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

True or False

The domain of the exponential function

$f (x) = a^{x}$ where $a > 0, a \neq 1$ is the set of all real numbers.

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

$A (n)$ ________ is a function of the form $f (x) = C a^{x}$ where $a > 0, a \neq 1,$ and $C \neq 0$ are real numbers. The base $a$ is a ____ and $C$ is a _____.

The graph of an exponential function is given. Match each graph to one of the following functions.

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

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

See all solutions

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