A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
solve for x
7(1/2)^x=2x
anonymous
 5 years ago
solve for x 7(1/2)^x=2x

This Question is Closed

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0gotta do logs and exponents :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0take the log of each side: log[(7)(1/2)^x] = log(2x) ; now seperate the logs into addition. log(7) + log((1/2)^x) = log(2) + log(x)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0remember the log(AB) = log(A) + log(B)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0also log(N^x) = x log(N)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok thanks i think i can get it now

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Erm, unless I am missing something, that cannot be solved exactly; only through iterations.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0log(7) + x log(1/2) = log(2) + log(x) log(7) + x log(1)  x log(2) = log(2) + log(x) [x log(1)  x log(2)] log(x) = log(2)  log(7) x log(1)  x log(2)   = log(2/7) log(x) log(x) log[(1^x)/x]  log[(2^x)/x] = log(2/7) log [(1^x)/(2^x)] = = log(2/7) (1^x)/(2^x) = 2/7 7(1^x) = 2(2^x) this is my stuff so far :) might be helpful

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The answer is about 1.362, but it's unlikely you'll be able to solve it much better.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0maybe change of base? thats what I was thinking....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It cannot be solved. You made a mistake.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i probably did :) can you point it out?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0[x log(1)  x log(2)] log(x) = log(2)  log(7) x log(1)  x log(2)   = log(2/7) log(x) log(x) Wanna explain what you did here? I may be missing it, but rest assured there is a mistake somewhere, as what you got to can be solved (exactly), but what you started with cannot.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Either way, the next line also doesn't follow.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i was thinking along the lines of log(a)  log(b) = log(a/b) log(1^x)  log(2^x)  split the fraction? log(x)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0log[(1^x/2^x)/x] would that be right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0newton has the right answer but im just not seeing how to solve for it

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0another way of looking at it is: 1^x 2x  =  2^x 7

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, its the playing around with the numbers and rules that I like to practice :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0(1/2)^x = 2x/7 is right, but you can't go beyond that (in elementary functions for an exact answer; only iterations will get you a nearish result)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh, wait, of course that is right, it's almost exactly as given. Doh. But yeah, no solution, bad question

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0im just lost on isolating the x. so say if you had 3^X=2X how would i isolate x

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0take log3 of each side maybe as a start?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x = log3(2x) x = log3(2) + log3(x) stuff like that

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You cannot do it. See ' Lambert W Function ' .

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0or find a convient "base" and see if you can manipulate it...... its always fun to try the impossible :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Depending on the level, you are almost certainly meant to iterate this to get nearer and nearer to the root.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.03^3^X = 3^2X 3^3X = 3^2X .... is that allowed?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Nope (and for the record, 3^x = 2x has no real solutions at all, regardless of method). 3^(3^2) = 3^9 3^(3*2) = 3^6

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0(a^b)^c = a^(bc) =/= a^(b^c), in general

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Wow. So you can't use logarithms for this solution effectively? No solution.. agh. >.<
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.