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Chapter 5: Q. 65 (page 284)

Solve the equation ${(\frac{1}{5})}^{x} = \frac{1}{25}$
and verify your results using a graphing utility.

Short Answer

Expert verified

Required solution set is {2}.

Step by step solution

01

Step 1. Given information

${(\frac{1}{5})}^{x} = \frac{1}{25}$

02

Step 2. Calculations

${(\frac{1}{5})}^{x} = \frac{1}{25} 5^{- x} = 5^{- 2} i f a^{u} = a^{v} t h e n u = v x = 2$

03

Step 3. Graphing solution

Graph $y = {\frac{1}{5}}^{x}$ and y =1/25 intersect at (2,0.04)

Hence the required solution set is {2}.

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Most popular questions from this chapter

The domain of a one-to-one functionf is $[5, \infty)$ , and its range is $[- 2, \infty)$ . State the domain and the range of $f^{- 1}$ .

Begin with the graph of $y = e^{x}$ and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

localid="1646160286433" $f (x) = 5 - e^{- x}$

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 function $f (x) = \frac{2 x}{x - 3}$ has $y = 2$ as a horizontal asymptote.

If $f (x) = a^{x}$ , show that $f (A + B) = f (A) . f (B)$ .

Begin with the graph of $y = e^{x}$ and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

$f (x) = - e^{x}$

See all solutions

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