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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q. 13 (page 352)

Solve the equation 4^x-3 = 8^2x.

Short Answer

Expert verified

Value of $x i s - \frac{3}{2}$

Step by step solution

01

Step 1. Given Information:

Given Equation: 4^x-3 = 8^2x

We want to solve the given equation for value of x.

02

Step 2. Solution

Notice how bases 4 and 8 can be reduced to the same base, which is a = 2.

We will use the property ${(a^{m})}^{n} = a^{m 路 n}$

role="math" localid="1647415498328" $4^{x - 3} = 8^{2 x} {(2^{2})}^{x - 3} = {(2^{3})}^{2 x} 2^{2 (x - 3)} = 2^{3 路 2 x} 2^{2 x - 6} = 2^{6 x}$

Now that we have reduced the expressions to equal bases we will use the following property:

role="math" localid="1647415462256" $I f a^{x} = a^{y}, t h e n x = y (w h e r e a 鈮� 1 a n d a > 0) - - - (1)$

Using the property (1) we get

$2^{2 x - 6} = 2^{6 x} 2 x - 6 = 6 x 2 x - 6 x = 6 - 4 x = 6 x = - \frac{3}{2}$

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Most popular questions from this chapter

solve each equation. Verify your results using a graphing utility.

$9^{- x + 15} = 27^{x}$

A function $f$ has an inverse function. If the graph of $f$ lies in quadrant I in which quadrant does the graph of $f^{- 1}$ lie?

If $2^{x} = 3$ , what does $4^{- x}$ equal?

In Problems $33 - 40$ , the graph of an exponential function is given. Match each graph to one of the following functions.

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

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

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