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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

01

Step 1. Given information.

Consider the given information.

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

02

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

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

$3^{x^{2} - 7} = 27^{2 x}$

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

Solve:

$x^{2} + 3 x = 4$ x

Determine the exponential function whose graph is given.

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

$f (x) = - \frac{2 x}{x - 1}$

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

See all solutions

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