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Chapter 5: Q 57. (page 309)

Write each expression as a single logarithm.
$3 \log_{5} u + 4 \log_{5} v$

Short Answer

Expert verified

The result is $\log_{5} (u^{3} v^{4})$ .

Step by step solution

Step 1. Given information.

Consider the given information.

$3 \log_{5} u + 4 \log_{5} v$

Step 2. Calculation.

Apply the property $\log_{a} (M N) = \log_{a} M + \log_{a} N$ .

$\begin{array}{rcl} 3 \log_{5} u + 4 \log_{5} v & = & \log_{5} u^{3} + \log_{5} v^{4} \\ = & \log_{5} (u^{3} v^{4}) \end{array}$

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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.

True or False

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

The domain of a one-to-one functiong is $(- \infty, 0)$ , and its range is $[0, \infty)$ . State the domain and the range of $g^{- 1}$ .

Do you think that there is a power function that increases

more rapidly than an exponential function whose base is greater than 1 ? Explain.

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?

A function $y = f (x)$ is increasing on the interval $(0, 5) .$ What conclusions can you draw about the graph of $y = f^{- 1} (x)$ ?

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Write each expression as a single logarithm.
$3 \log_{5} u + 4 \log_{5} v$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

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Write each expression as a single logarithm.3log5u+4log5v

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Discrete Mathematics

Probability and Statistics

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Write each expression as a single logarithm.
$3 \log_{5} u + 4 \log_{5} v$