MHB Logarithm inequality divide an inequality by a negative value

Click For Summary
The discussion centers on the error in handling logarithmic inequalities when dividing by a negative value. Specifically, it highlights that since \(\log_{10}\left(\frac{1}{2}\right)<0\), dividing the inequality by a negative number necessitates reversing the inequality direction. This leads to the conclusion that the correct interpretation results in \(2<3\). Understanding this principle is crucial for accurately solving logarithmic inequalities. Properly applying this rule prevents misinterpretation of results in mathematical expressions.
highmath
Messages
35
Reaction score
0
What is error in the picture?
 

Attachments

  • logaritmquestion.PNG
    logaritmquestion.PNG
    7.9 KB · Views: 96
Mathematics news on Phys.org
The error arises because:

$$\log_{10}\left(\frac{1}{2}\right)<0$$

When we divide an inequality by a negative value, we need to reverse the direction of the inequality, so that we get:

$$2<3$$
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Undergrad What Are the Benefits of Triangle Inequality in Mathematics?
  • · Replies 2 ·
Replies
2
Views
2K
High School What Are Basic Questions About Understanding Inequalities?
  • · Replies 12 ·
Replies
12
Views
2K
MHB How to Graph a System of Inequalities for Investment Allocation?
  • · Replies 16 ·
Replies
16
Views
2K
High School Why is pH a negative logarithm?
  • · Replies 5 ·
Replies
5
Views
5K
High School The same inequality, but two equivalent ways to express it
  • · Replies 14 ·
Replies
14
Views
2K
MHB *gre.al.9 GRE Exam Inequality with modulus or absolute value
  • · Replies 4 ·
Replies
4
Views
2K
High School Characteristics of the parent logarithmic function
  • · Replies 4 ·
Replies
4
Views
3K
MHB Proof of Inequality: $|a+b| \leq |a| + |b|$
  • · Replies 8 ·
Replies
8
Views
2K
MHB Overcoming Struggles to Addressing Inequalities Step by Step
  • · Replies 3 ·
Replies
3
Views
1K
MHB Can You Solve This Challenging Inequality Problem?
  • · Replies 1 ·
Replies
1
Views
2K