/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 9 Find a number \(x\) such that \(... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 9

Find a number \(x\) such that \(\ln x=-2\).

Short Answer

Expert verified
The solution to the equation \(\ln x = -2\) is \(x \approx \frac{1}{7.389}\).

Step by step solution

01

Rewrite the equation using the exponential function

To find the value of x, we will need to rewrite the equation \( \ln x = -2\) using the exponential function. The exponential function is the inverse of the natural logarithm function, so we can express x as \(e\) raised to the power of -2. We can write this as: \[x = e^{-2}\]
02

Calculate the value of x

Now, we need to find the value of x that satisfies the equation \(x = e^{-2}\). To do this, we will need to evaluate the exponential expression: \[x = e^{-2} = \frac{1}{e^2} \]
03

Simplify the expression

Now, we can simplify the expression by evaluating \(e^2\) and expressing the result as a fraction: \[x = \frac{1}{e^2} = \frac{1}{7.389} \]
04

Present the solution

We have found the value of x that satisfies the equation \(\ln x = -2\): \[x \approx \frac{1}{7.389}\] So, the solution to the given problem is \(x \approx \frac{1}{7.389}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Estimate the indicated value without using a calculator. \(e^{-0.00046}\)

Find a number \(w\) such that \(\ln (3 w-2)=5\).

Show that \(\cosh x \geq 1\) for every real number \(x\).

Suppose \(x\) is a positive number. (a) Explain why \(x^{t}=e^{t \ln x}\) for every number \(t\). (b) Explain why $$ \frac{x^{t}-1}{t} \approx \ln x $$ if \(t\) is close to 0

Find all numbers \(x\) that satisfy the given equation. \(\ln (x+5)+\ln (x-1)=2\)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.