/*! 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 66 Use properties of logarithms to ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 66

Use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(1 .\) Where possible, evaluate logarithmic expressions without using a calculator. $$\frac{1}{3}\left(\log _{4} x-\log _{4} y\right)+2 \log _{4}(x+1)$$

Short Answer

Expert verified
The condensed logarithmic expression is \( \log_4 \left(\left(\frac{x}{y}\right)^{1/3} \times \left(x+1\right)^2\right) \).

Step by step solution

01

Applying Logarithm Subtraction Rule

The logarithm subtraction rule states that \( \log_b a - \log_b c = \log_b (a/c) \). Hence, the expression becomes \( \frac{1}{3} \log_4 \left(\frac{x}{y}\right) + 2 \log_4 (x+1) \).
02

Utilize the Logarithm Power Rule

The logarithm power rule states that \( n \log_b a = \log_b (a^n) \). Applying this, the simplified expression is \( \log_4 \left(\frac{x}{y}\right)^{1/3} + \log_4 \left(x+1\right)^2 \).
03

Applying Logarithm Addition Rule

The logarithm addition rule states \( \log_b a + \log_b c = \log_b (a * c) \). Using this rule, the final expression becomes \( \log_4 \left(\left(\frac{x}{y}\right)^{1/3} \times \left(x+1\right)^2\right) \).

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

Explain how to solve an exponential equation when both sides cannot be written as a power of the same base. Use \(3^{x}=140\) in your explanation.

Use a calculator with \(a\left[y^{x}\right]\) key or \(a \square\) key to solve. The 1986 explosion at the Chernobyl nuclear power plant in the former Soviet Union sent about 1000 kilograms of radioactive cesium-137 into the atmosphere. The function \(f(x)=1000(0.5)^{\frac{x}{30}}\) describes the amount, \(f(x),\) in kilograms, of cesium-137 remaining in Chernobyl \(x\) years after 1986 If even 100 kilograms of cesium- 137 remain in Chernobyl's atmosphere, the area is considered unsafe for human habitation. Find \(f(80)\) and determine if Chernobyl will be safe for human habitation by 2066

Determine whether each statement makes sense or does not make sense, and explain your reasoning. After 100 years, a population whose growth rate is \(3 \%\) will have three times as many people as a population whose growth rate is \(1 \%\)

You take up weightlifting and record the maximum number of pounds you can lift at the end of each week. You start off with rapid growth in terms of the weight you can lift from week to week, but then the growth begins to level off. Describe how to obtain a function that models the number of pounds you can lift at the end of each week. How can you use this function to predict what might happen if you continue the sport?

This will help you prepare for the material covered in the first section of the next chapter. $$\text { Solve: } \frac{5 \pi}{4}=2 \pi x$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

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.