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Chapter 5: Q 42. (page 308)

Write each expression as a sum and/or difference of logarithms. Express powers as factors.
$\ln (\frac{e}{x})$

Short Answer

Expert verified

The result is $1 - \ln x$ .

Step by step solution

01

Step 1. Given information.

Consider the given information.

$\ln (\frac{e}{x})$

02

Step 2. Calculation.

Apply the logarithm property to simplify.

$\begin{array}{rcl} \ln (\frac{e}{x}) & = & \ln e - \ln x \\ = & 1 - \ln x \end{array}$

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Most popular questions from this chapter

the function f is one-to-one. Find its inverse and check your answer.

$f (x) = \frac{x^{2} + 3}{3 x^{2}} x > 0$

The graph of an exponential function is given. Match each graph to one of the following functions.

If $f (x) = 2 x^{2} + 5$ and $g (x) = 3 x + a$ , find $a$ so that the graph of $f \circ g$ crosses the y-axis at 23.

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

$4^{x} 2^{x^{2}} = 16^{2}$

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

Find the average rate of change of $f (x) = 3 x - 5$ from $x = 0 t p x = 4$

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