/*! 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 48 Write as the sum or difference o... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 48

Write as the sum or difference of logarithms and simplify, if possible. Assume all variables represent positive real numbers. $$\log _{2} \frac{m^{5}}{m^{2}+3}$$

Short Answer

Expert verified
\(\log _{2} \frac{m^{5}}{m^{2}+3} = 5\log _{2}(m) - \log _{2}(m^2 + 3)\)

Step by step solution

01

Use the quotient rule for logarithms

The quotient rule states that for any positive real numbers M and N, and any positive real number b: \(\log _{b} \frac{M}{N} = \log _{b} M - \log _{b} N\). In our case, M is \(m^5\) and N is \(m^2 + 3\). Using this rule, we rewrite the given expression as follows: \(\log _{2} \frac{m^{5}}{m^{2}+3} = \log _{2}(m^5) - \log _{2}(m^2 + 3)\)
02

Apply the power rule for logarithms

The power rule states that for any positive real number M, any positive real number b, and any real number r: \(\log _{b}(M^r) = r\log _{b} M\). In our case, we have \(\log _{2}(m^5)\). Using the power rule, we have: \(\log _{2}(m^5) = 5\log _{2}(m)\)
03

Combine the results and write the final expression

Substituting the expression obtained in Step 2 into the result from Step 1, we have: \(\log _{2} \frac{m^{5}}{m^{2}+3} = 5\log _{2}(m) - \log _{2}(m^2 + 3)\) And that's our final expression, written as the sum or difference of simplified logarithms in base 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 logarithm. Assume the variables are defined so that the variable expressions are positive and so that the bases are positive real numbers not equal to \(1 .\) $$\log _{7} 8-4 \log _{7} x-\log _{7} y$$

Find the inverse of each one-to-one function. $$g(x)=\sqrt{x+3}, x \geq-3$$

Given that \(\log 5=0.6990\) and \(\log 9=0.9542,\) use the propertics of logarithms to approximate the following $$\log \frac{9}{5}$$

Use the formula \(A=P e^{r t}\). Cynthia wants to invest some money now so that she will have \(\$ 5000\) in the account in 10 yr. How much should she invest in an account earning \(8 \%\) compounded continuously?

Solve equation. \(\log _{6} 40 x-\log _{6}(1+x)=2\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

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.