Q. 41 Solve each exponential equation.... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q. 41 (page 315)

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility
$3^{1 - 2 x} = 4^{x}$

Short Answer

Expert verified

$x = \frac{\ln 3}{2 \ln 3 + \ln 4} 鈮� 0.307$

Step by step solution

Step 1. Given informaiton

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility

$3^{1 - 2 x} = 4^{x}$

Step 2. Explanation

$\begin{array}{l} Firstwenoticethatthebasearenoteaqual. \\ Soweneedtousethistwoproperties. \\ 鈬� {logl}_{a} M^{r} = r \log_{a} M \\ 鈬� {IfM=Nthanlog}_{a} M = {log}_{a} N \\ {Foreasiercalculationwewillusethenaturallogarithmlog}_{e} x = \ln x \\ 鈬� 3^{1 鈭� 2 x} = 4^{x} \\ 鈬� \ln 3^{1 鈭� 2 x} = \ln 4^{x} \\ 鈬� (1 鈭� 2 x) \ln 3 = x \ln 4 \\ 鈬� \ln 3 鈭� 2 x \ln 3 = x \ln 4 \\ 鈬� 鈭� 2 x \ln 3 鈭� x \ln 4 = 鈭� \ln 3 \\ 鈬� 鈭� (2 \ln 3 + \ln 4) = 鈭� \ln 3 \\ 鈬� x = \frac{\ln 3}{2 \ln 3 + \ln 4} 鈮� 0.307 \end{array}$

Step 3. Verify the solution with the graph.

The graph of the given function is:

Here we see that the graph is a straight line passes through the point $x = 0.307$ .

Thus it is verified that the solution is correct.

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91影视

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility
$3^{1 - 2 x} = 4^{x}$

Short Answer

Step by step solution

Step 1. Given informaiton

Step 2. Explanation

Step 3. Verify the solution with the graph.

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91影视

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility 31-2x=4x

Short Answer

Step by step solution

Step 1. Given informaiton

Step 2. Explanation

Step 3. Verify the solution with the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Mechanics Maths

Probability and Statistics

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility
$3^{1 - 2 x} = 4^{x}$