My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion


Thanks Tree3Thanks
  • 1 Post By AplanisTophet
  • 1 Post By idontknow
  • 1 Post By gedmathbootcamp
Reply
 
LinkBack Thread Tools Display Modes
June 1st, 2019, 04:20 AM   #1
Senior Member
 
Joined: Dec 2015
From: somewhere

Posts: 534
Thanks: 81

Solve for integers

Solve the equation for $\displaystyle n\in \mathbb{N} ; $.
$\displaystyle 2n=2^n $.
idontknow is offline  
 
June 1st, 2019, 06:52 AM   #2
Senior Member
 
Joined: Jun 2014
From: USA

Posts: 528
Thanks: 42

$n = 1, 2$

That seems too easy. What’s the catch?
Thanks from topsquark
AplanisTophet is offline  
June 2nd, 2019, 03:51 AM   #3
Senior Member
 
Joined: Dec 2015
From: somewhere

Posts: 534
Thanks: 81

n must be power of 2 which gives $\displaystyle 2^k =k+1 $ .
k=0 and 1 .
Thanks from topsquark
idontknow is offline  
June 2nd, 2019, 01:17 PM   #4
Newbie
 
Joined: Jun 2019
From: US

Posts: 1
Thanks: 1

The answers are n = 1 and n = 2. n=0 doesn't work because n is not a natural number, also if n is 0 we get 0 = 1 which is not true.

The question says that N must be a natural number, that means 1,2,3,4,.....

The strategy here is to start trying beginning with the smallest n. Try 1, it works, try 2, it also works. If we try 3, we get
6 = 8, that doesn't work.
Try 4 we get 4 = 16, that also doesn't work.

We can see that the right side grows faster than the left as n increases, so no number higher than 2 will work.

The only solutions are 1 and 2
Thanks from topsquark

Last edited by gedmathbootcamp; June 2nd, 2019 at 01:26 PM.
gedmathbootcamp is offline  
June 2nd, 2019, 06:23 PM   #5
Senior Member
 
Joined: Aug 2012

Posts: 2,321
Thanks: 714

Quote:
Originally Posted by gedmathbootcamp View Post

The question says that N must be a natural number, that means 1,2,3,4,.....
$0$ is not a solution of $\displaystyle 2n=2^n $ regardless of which convention you use for whether $0 \in \mathbb N$. The left hand side is $0$ and the right hand side is $1$.
Maschke is offline  
Reply

  My Math Forum > High School Math Forum > Elementary Math

Tags
integers, solve



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Integers yo79 Math Events 4 March 17th, 2013 12:50 AM
Solve in integers x,y. ultramegasuperhyper Number Theory 4 May 24th, 2011 09:19 PM
Solve in possitive integers Sara so Number Theory 3 November 12th, 2010 12:18 PM
integers Julie13 Calculus 0 August 18th, 2010 10:08 PM
Integers: cafegurl Elementary Math 3 January 7th, 2009 07:21 AM





Copyright © 2019 My Math Forum. All rights reserved.