/*! 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 53 Use the properties of logarithms... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 53

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $$\ln x y z^{2}$$

Short Answer

Expert verified
The expression \(\ln xyz^2\) expanded as a sum, difference, and/or constant multiple of logarithms is \(\ln x + \ln y + 2\ln z\).

Step by step solution

01

Identify the Operations

In the expression \(\ln xyz^2\), we can see that there is a multiplication between \(x\), \(y\), and \(z^2\). In addition to this, the variable \(z\) is raised to the power of 2.
02

Apply the Property of Logarithms for Multiplication

The property of logarithms for multiplication states that \(\ln (ab) = \ln a + \ln b\) for any two positive numbers \(a\) and \(b\). Applying this to the expression gives us: \(\ln xyz^2 = \ln x + \ln y + \ln z^2\)
03

Apply the Property of Logarithms for Exponents

The property of logarithms for exponents states that \(\ln a^b = b \ln a\) for any positive number \(a\) and any real number \(b\). Applying this to \(\ln z^2\) gives us: \(\ln xyz^2 = \ln x + \ln y + 2\ln z\)

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

Complete the table for the time \(t\) (in years) necessary for \(P\) dollars to triple if interest is compounded continuously at rate \(r\). $$ \begin{array}{|l|l|l|l|l|l|l|} \hline r & 2 \% & 4 \% & 6 \% & 8 \% & 10 \% & 12 \% \\ \hline t & & & & & & \\ \hline \end{array} $$

Use a graphing utility to graph and solve the equation. Approximate the result to three decimal places. Verify your result algebraically. $$\ln (x+1)=2-\ln x$$

Is it possible for a logarithmic equation to have more than one extraneous solution? Explain.

Rewrite each verbal statement as an equation. Then decide whether the statement is true or false. Justify your answer. The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.

Use your school's library, the Internet, or some other reference source to write a paper describing John Napier's work with logarithms.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.