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Chapter 5: Q. 64 (page 284)

Solve the equation $3^{- x} = 81$
and verify your results using a graphing utility.

Short Answer

Expert verified

Required solution set is {-4}.

Step by step solution

01

Step 1. Given information

$3^{- x} = 81$

02

Step 2. Calculations

$3^{- x} = 81 3^{- x} = 3^{4} i f a^{u} = a^{v} t h e n u = v x = - 4$

03

Step 3. Graphing solution

Graph $y = 3^{- x}$ and y =81 intersect at (-4,81)

Hence the required solution set is {-4}.

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Most popular questions from this chapter

Solve the equation $2^{2 x - 1} = 4$

and verify your results using a graphing utility.

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

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.

$f (x) = e^{x + 2}$

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.

Use a calculator to compute the various values of the expression. Compare the values to e.

$2 + \frac{1}{1 + \frac{1}{2 + \frac{2}{3 + \frac{3}{4 + \frac{4}{e t c}}}}}$

See all solutions

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