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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q 16. (page 308)

Use properties of logarithms to find the exact value of each expression. Do not use a calculator.
$\ln e^{\sqrt{2}}$

Short Answer

Expert verified

The value is $\sqrt{2}$ .

Step by step solution

01

Step 1. Given information.

Consider the given information.

$\ln e^{\sqrt{2}}$

02

Step 2. Logarithm properties.

The properties are defined as,

$\begin{array}{l} \log_{a} a = 1 \\ \log (M N) = \log_{a} M + \log_{a} N \\ \log_{a} (\frac{M}{N}) = \log_{a} M - \log_{a} N \\ \log_{a} M^{r} = r \log_{a} M \end{array}$

03

Step 3. Calculation.

Apply the properties.

\begin{array}{rcl} \ln e^{\sqrt{2}} & = & \sqrt{2} \ln e \\ = & \sqrt{2} (1) \\ = & \sqrt{2} \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.

solve each equation

$9^{2 x} 27^{x^{2}} = 3^{- 1}$

True or False $f (g (x)) = f (x) . g (x)$ .

Evaluate each expression using the graphs of $y = f (x)$ and $y = g (x)$ shown in the figure.

(a) $(g 鈭� f) (- 1)$ (b) $(g 鈭� f) (0)$ (c) $(f 鈭� g) (- 1)$ (d) $(f 鈭� g) (4)$ .

Solve given equation and verify your result using graphing utility.

$e^{x^{2}} = e^{3 x} . \frac{1}{e^{2}}$

See all solutions

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