• Support PF! Buy your school textbooks, materials and every day products Here!

Minimum value of logarithmic equation

  • Thread starter ritwik06
  • Start date
  • #1
580
0

Homework Statement



For x>1, find the minimum possible value of [tex]2 log_{2}x-log_{x}(0.01)[/tex]

The Attempt at a Solution


Greater the value of x, greater is the value of expression. Right?
I tried to differentiate it, but it was no help. The derivative becomes zero when |log x|=[tex]\sqrt{log 2}[/tex]

Help me further.
 

Answers and Replies

  • #2
Defennder
Homework Helper
2,591
5


What did you get when you differentiate it?
 
  • #3
580
0


What did you get when you differentiate it?
Why do ya ask that? Is it wrong?
I got:
2*(1/x ln 2)-2*(1/log^{2} x)*(1/(x ln 10))
 
  • #4
Defennder
Homework Helper
2,591
5


Well, apparently I can't tell if it's correct unless I know your working. I can't read what you wrote that. Is it [tex]\frac{2 \ln x}{\ln 2} - \frac{2}{\log_2 x} \left( \frac{1}{x \ln 10} \right) [/tex].

If so then I don't think it's correct.
 
  • #5
580
0


Well, apparently I can't tell if it's correct unless I know your working. I can't read what you wrote that. Is it [tex]\frac{2 \ln x}{\ln 2} - \frac{2}{\log_2 x} \left( \frac{1}{x \ln 10} \right) [/tex].

If so then I don't think it's correct.
[tex]\frac{2}{x ln 2}-\frac{2}{(log^{2} x)*(x ln 10)}[/tex]
 
  • #6
dynamicsolo
Homework Helper
1,648
4


This problem sets a similar trap to that of another problem you asked about. It would make life easier if you rewrote the [tex]log_{x}(0.01)[/tex] term as a log-base-2 term first, so you could combine it with the first term...

(You could grind through the differentiation you have, but it is a rather cumbersome "hammer" to use on the problem.)
 
  • #7
308
0


I got:
[tex]\frac{2}{x ln 2}-\frac{2 ln 10}{x ln^2 x}[/tex]
for the derivative.
I set it equal to zero, cross multiplied and came up with:

[tex]ln^2x=ln 10 ln 2[/tex]

Dunno if that helps...your derivative was different than mine.
CC
 
Last edited:
  • #8
580
0


rewriting:
[tex]2log_{2}x+\frac{2(1+log_{2}5)}{log_{2}x}[/tex]
 
  • #9
308
0


Take the square root of both sides, ignore the absolute value bars, because for x>1 the thing is positive, then take the exponential of both sides. I got x=3.53722.......
plug that back in to get the y value.
CC
 
Last edited:

Related Threads on Minimum value of logarithmic equation

  • Last Post
Replies
8
Views
984
Replies
38
Views
3K
  • Last Post
Replies
9
Views
1K
  • Last Post
Replies
15
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
16
Views
2K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
7
Views
3K
Top