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Chapter 5: Q 10. (page 308)

True or false $\log (x + 3) - \log (2 x) = \frac{\log (x + 3)}{\log (2 x)}$

Short Answer

Expert verified

This is false.

Step by step solution

Step 1. Given information.

Consider the given information.

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

Step 2. Calculation.

Consider the left side of the equation.

$\log (x + 3) - \log (2 x)$

Apply the logarithm property.

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

Step 3. Conclusion.

Since the left side is not equal to the right side.
The equation is not true.

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Most popular questions from this chapter

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

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and verify your results using a graphing utility.

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Solve given equation and verify your result using graphing utility.

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Vehicle Stopping Distance Taking into account reaction time, the distance $d$ (in feet) that a car requires to come to a complete stop while traveling $r$ miles per hour is given by the function

localid="1646198784356" $d (r) = 6.97 r - 90.39$

a. Express the speed $r$ at which the car is traveling as a function of the distance localid="1646198792401" $d$ required to come to a complete stop

b. Verify that localid="1646198797631" $r = r (d)$ is the inverse of localid="1646198802104" $d = d (r)$ by showing that localid="1646198806352" $r (d (r)) = r$ and localid="1646198811055" $d (r (d)) = d$

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$d (r (d)) = d$

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True or false $\log (x + 3) - \log (2 x) = \frac{\log (x + 3)}{\log (2 x)}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 3. Conclusion.

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Most popular questions from this chapter

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True or falselogx+3-log2x=logx+3log2x

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 3. Conclusion.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Geometry

Discrete Mathematics

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

True or false $\log (x + 3) - \log (2 x) = \frac{\log (x + 3)}{\log (2 x)}$