/*! 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 108 Without showing the details, exp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 108

Without showing the details, explain how to condense \(\ln x-2 \ln (x+1)\)

Short Answer

Expert verified
The condensed form of the expression \(\ln x-2 \ln (x+1)\) is \(\ln (x/(x+1)^2)\

Step by step solution

01

Apply the multiplication property of Logarithms

Applying the multiplication property of logarithms which states \( a \ln b = \ln (b^a) \) to the second term \(-2 \ln (x+1)\), it turns into \(- \ln (x+1)^2\)
02

Apply the division property of Logarithms

The expression now becomes \( \ln x - \ln (x+1)^2\). Now, apply the division property of logarithms that states \( \ln a - \ln b = \ln (a/b) \) to this expression, it simplifies to \(\ln (x/(x+1)^2)\)
03

Final Answer

The condensed form of the expression \(\ln x-2 \ln (x+1)\) is thus \(\ln (x/(x+1)^2)\)

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

Write as a single term that does not contain a logarithm: \(e^{\ln 8 x^{3}-\ln 2 x^{2}}\)

Find the domain of each logarithmic function. $$ f(x)=\ln \left(x^{2}-x-2\right) $$

Evaluate each expression without using a calculator. $$ \log _{2}\left(\log _{3} 81\right) $$

Find the domain of each logarithmic function. $$ f(x)=\log \left(\frac{x-2}{x+5}\right) $$

Find the domain of each logarithmic function. $$ f(x)=\log _{5}(x+4) $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

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.