/*! 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 139 Determine whether each statement... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 139

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{\log _{2} 8}{\log _{2} 4}=\frac{8}{4}$$

Short Answer

Expert verified
The statement \(\frac{\log_{2} 8}{\log_{2} 4}=\frac{8}{4}\) is false. The true statement should be \(\frac{\log_{2} 8}{\log_{2} 4} = \frac{3}{2}\).

Step by step solution

01

Solve Logarithmic Expressions

It's important to remember that logarithms are the inverse operations of exponential functions. Thus, \(\log_{2} 8\) simplifies to 3 because 2 raised to the power of 3 is equal to 8, and \(\log_{2} 4\) simplifies to 2 because 2 raised to the power of 2 is equal to 4. Hence, the given equation becomes \(\frac{3}{2}\).
02

Compare to Incorrect Part of the Equation

Now, emphasizing on the incorrect part of the original equation that is \(\frac{8}{4}\), which simplifies to 2. It can be observed that \(\frac{3}{2}\) does not equal to 2.
03

Provide the Correct Statement

To provide a correct statement, replace \(\frac{8}{4}\) with \(\frac{3}{2}\). This gives us the true equation: \(\frac{\log_{2} 8}{\log_{2} 4}=\frac{3}{2}\).

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

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\text { The domain of } f(x)=\log _{2} x \text { is }(-\infty, \infty)$$.

Graph \(f\) and \(g\) in the same viewing rectangle. Then describe the relationship of the graph of g to the graph of \(f\). $$f(x)=\log x, g(x)=\log (x-2)+1$$

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?

Describe the shape of a scatter plot that suggests modeling the data with an exponential function.

Graph \(x+2 y=2\) and \(x-2 y=6\) in the same rectangular coordinate system. At what point do the graphs intersect? $$ \text { Solve: } 5(2 x-3)-4 x=9 $$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Probability and Statistics

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.