Solving the logarithimic inequality log_2(x)/(2) + (log_2x^2)/(log_2 (2/x)) <= 1 several times but keeping getting wrong answers.

kadejoset 2022-07-15 Answered
Solving the logarithimic inequality log 2 x 2 + log 2 x 2 log 2 2 x 1
I tried solving the logarithmic inequality:
log 2 x 2 + log 2 x 2 log 2 2 x 1
several times but keeping getting wrong answers.
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 (2)

Selden1f
Answered 2022-07-16 Author has 14 answers
Let log 2 x = A, then log 2 x 2 = 2 log 2 x = 2 A and log 2 2 x = log 2 2 log 2 x = 1 A. So the given inequality becomes:
( A 1 ) + 2 A 1 A 1.
Consequently we get
4 A A 2 1 1 A 1.
Furthermore you get
5 A A 2 2 1 A 0.
Hopefully you can solve from here.

We have step-by-step solutions for your answer!

kominis3q
Answered 2022-07-17 Author has 2 answers
Put u = log 2 ( x 2 ) = log 2 x 1
Note that log 2 ( x 2 ) = 2 ( u + 1 ), and log 2 ( 2 x ) = u
Hence inequality becomes
u 2 ( u + 1 ) u 1 u 2 3 u 2 u 0 ( u α ) ( u β ) u 0
where α = 3 + 17 2 ,   β = 3 17 2  
u β ,   0 u α ,   log 2 ( x 2 ) 3 17 2 ,   0 log 2 ( x 2 ) 3 + 17 2 log 2 x 5 17 2 ,   1 log 2 x 5 + 17 2
As x > 0,
0 < x 2 5 17 2 ,   2 x 2 5 + 17 2

We have step-by-step solutions for your answer!

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 2022-06-01
What are the basic, fundamental concepts of logarithms?
Soon I will be learning of logarithms, but I wish to have a head start over my class mates or at least a fair greeting to the concept. I would appreciate a very clear-cut answer with very straight to the point examples, an answer like this and with steps would be tremendously helpful and quickly voted best answer. Some specific questions on which to base your answer could be: why are they used? What is an example of a simple logarithm? how do you solve one?, and how does it apply to quadratic equations? Thanks in advance.
asked 2022-04-15
Is 112+1314+15=ln2 true?
asked 2022-07-17
Logarithmic Contest Question
The Problem was as follows:
Define log ( n ) to be the smallest number of times the log function must be iteratively applied to n to get a result less than or equal to 1. For example log ( 1000 ) = 2 since l o g ( 1000 ) = 3 and l o g ( 3 ) = 0.477 1. Let a be the smallest integer such that log ( a ) = 3. Computer the number of zeroes in the base 10 representation of a
My answer was 10 10 but they claimed it to be 9
My logic was that log 10 10 10 = 10 10 and log 10 10 = 10 and log 10 = 1 and 1 1 so the log 10 10 10 = 3
I presume this means that a smaller answer exists, or I made a logic error somewhere. Can someone show how the smallest answer has 9 zeroes?
asked 2022-06-26
Is anyway to prove this: k = 1 n ( a k ) < ( 1 / n n ) ( k = 1 n ( 1 + a k a k + 1 ) ) n
ak and n are positive real number greater than 0.
EDIT: a_{k+1} becomes a_{1} when a_{k}=a_{n}, it is a cylic notation. SORRY.
Any ideas of how to attack the problem?? Thank You.
I don't know if this could help, but the 1/n is also the exponent for the left hand side. I'm thinking maybe of log??
I'm pretty sure that at some point it would be helpful the binominal coefficent?? I don't know.
asked 2022-09-06
Evaluate. 8 3 x = 360
asked 2022-04-11
Use the properties oflogarithms to simplify the expression.
3x+1=27
asked 2022-09-24
Limit of log with factor
Problem
If
lim n f ( n ) log n log log n = y
where f is some function, does this imply that
lim n f ( n ) log ( x n ) log log n = y
for some x O ( 1 )? Or does this give another Limit y?
Progress
For y = 0 or y = ± , I think, this factor x should not change anything, but for y ( , 0 ) ( 0 , ), I think this Limit should change, shouldn't it?