How do I simplify and calculate this inequality? log &#x2061;<!-- ⁡ --> ( x

sebadillab0 2022-07-08 Answered
How do I simplify and calculate this inequality?
log ( x 3 ) > | x 1 |
I can't figure out how to go about solving this inequality, besides this one step:
3 log ( x ) > | x 1 |
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Allison Pena
Answered 2022-07-09 Author has 14 answers
As said in the comments, you have two situations buit you can notice that for x = 1, the lhs and rhs are equal.
So consider the case where x = 1 ϵ and use Taylor expansion for the lhs at x = 1. Yous will easily see that the inequality is not satisfied. Since you noticed that for x = 1, l h s = r h s, the inequality will be satisfied for x > 1. So, you can now forget the absolute value in the rhs.
Now, compute the derivative of l h s r h s; it is equal to 3 / x 1 and so canceled for x = 3; the second derivative being negative, then this point corresponds to a maximum. For x = 3, l h s = 3 l o g ( 3 ) and r h s = 2; so, at this point, l h s > r h s. On the other side, you know that x moves faster then l o g ( x ); so there is a point which will corresponds to an x intercept. You will then need to solve the equation
log ( x 3 ) = x 1
log ( x 3 ) = x 1
which does not any simple analytical solution. If you plot the function, you will see that the solution is close to x = 6.71
So, the inequality is satisfied for 1 < x < 6.71
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-06-03
Adding 1 to a/b?
I've been learning algebra 2 and came across a question telling me to add 1 to a b by finding the least common multiple of the divisors. So I got 1 b 1 b + a b that simplified is b b + a b . So then I added those two fractions together and got a b b I saw that the two b's cancelled each other out so I got a 1 which is a? How does adding 1 to a b get a, this doesn't seem to be right because 1 + 2 3 isn't 2 it's 1 and 2 3 . Am I doing something wrong or is this actually correct, if so can you explain to me why?
asked 2022-04-10
Expressing as a single fraction
I'm trying to improve my maths so I can sit the GRE this time next year.
I'm stuck on a really silly question:
Express as a single fraction:
3 x 2 y 7 y 4 x
I'm trying to find a common denominator to cancel out the bottom line. Am I on the right track?
asked 2022-07-06
Please help me understand this simple fraction
I got started learning about fractions a few days ago, The tutorial I'm using for this, is limited to fractions like this
g ) 7 12 × 8 21 = 2 9
Now as I'm trying to find further exercices, I keep stumbling upon fraction-based problems that are built like this one.
5.Myltiply.
a ) 5 1 4 × 2 2 3 = 14
What does the number on the left mean? I mean the huge 5 and huge 2. is it a whole + a fraction? like 5 + (1/4)??
I would like to further my research on this topic, but I don't know what the name of these types of fractions are.
receiving a link to a tutorial would be fine too, I just don't know what search terms to use.
Also why is the solution 14?
asked 2022-02-09
How do you simplify 23÷12?
asked 2021-09-18
Add the fractions. If possible, simplify your answer.
7a2+6a+9+8a29=?
asked 2022-05-20
Adding fractions of Groups of People
I understand the rules of adding fractions perfectly well. I know how to find common denominators, and understand why adding fractions without common denominators doesn't make sense.
But, today someone asked me about adding 5 6 and 21 28 . They were wondering why dividing the two factions and taking the average ( 0.8333 + 0.75 2 = 0.7917) was giving them a different value than adding them together, and then dividing ( 5 6 + 21 28 = 26 34 = 0.7647).
My initial reaction was the same as yours: I was taken aback by someone adding fractions in this way, and I gave a quick refresher of why this doesn't make sense, and how to properly add fractions.
I thought I had helped them fix their problem, until they gave more more context: The 5 6 was five people in a group of six who were observed washing their hands after a certain activity. The 21 28 was twenty-one out of twenty-eight people who were observed washing their hands after a certain activity. The goal was to find the total number of people who had washed their hands, as a fraction of the total number of observed people. So, 26 34 is actually correct in this case.
But, I'm still having trouble reconciling this with what I know about fractions. At least, what I think I know. Is there a term for these sorts of fractions? This isn't like having five slices of a six-slice pizza combined with twenty-one slices of a twenty-eight-slice pizza. This is like having one oven holding six pizzas, five of which have mushrooms, and another (huge) oven holding twenty-eight pizzas, twenty-one of which have mushrooms. What fraction of the pizzas have mushrooms? Is it 5 6 + 21 28 ? I don't think so.
Is there some terminology I'm forgetting here? Why am I getting so tripped up by this?
asked 2022-04-10
How to simplify 3 / 2
My textbook says to do the following steps to simplify the 3 / 2
3 / 2 = ( ( 3 / 2 ) × ( 2 / 2 ) ) = 6 / 4 = 6 / 4 = 6 / 2.
However, if the fourth step is valid (1. please explain why and 2. I specifically mean where you "split" the square root into two parts), then why can't you simply do:
3 / 2 = 3 / 2
3 / 2 = 3 / 2
Why wouldn't that be valid?
My point is, are the two fractions equivalent?