My Math Forum  

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

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
June 16th, 2017, 02:37 PM   #1
Newbie
 
Joined: Oct 2015
From: Greece

Posts: 24
Thanks: 0

Custom function help!

Hello!

Say I have a number x. I want to make a function which will take this number and add some value to it in order to make it power of two (the closest value that is a power of two).

f(x) --> (power of two)

x can be any integer number.

For example, if I have x = 1, then I must add to it 1 in order to make it power of two because (1+1 = 2). If x = 9, I must add 7 (9+7 = 16).

I tried, but I can't think of any mathematical way of doing it.

So my point is, how can I find which number I must add to x in order to create a new number that is gonna be power of two?

Thank you!

Last edited by skipjack; June 17th, 2017 at 02:18 AM.
babaliaris is offline  
 
June 16th, 2017, 02:52 PM   #2
Senior Member
 
Joined: Aug 2012

Posts: 1,414
Thanks: 342

How can we find the next largest power of $2$? Given $x$, its exact power of $2$ is $\log_2 x$ and the next integer power of $2$ is $2^{\lceil \log_2 x \rceil}$ where $\lceil \cdot \rceil$ is the ceiling function, by definition the integer greater than or equal to a given real number.

Then the difference function is $2^{\lceil \log_2 x \rceil} - x$.

For example with $x = 9$ we have:

* $\log_2 9 \approx 3.1699 \dots$ [Wolfram Alpha]

* $\lceil 3.1699 \dots \rceil = 4$

* $2^4 = 16$

* $16 - 9 = 7$

This method works for any positive real number, not just positive integers.

However we have problems if $x$ is negative.

For example what's the smallest power of $2$ greater than or equal to $-5$? Is it $\frac{1}{2}$, or $\frac{1}{4}$, or $\frac{1}{8}$? There is no "next" power of $2$ greater than $-5$. I'm too lazy at the moment to sort this out in terms of complex logs but if we stick to real numbers, then $x$ has to be strictly positive.

Last edited by Maschke; June 16th, 2017 at 03:13 PM.
Maschke is offline  
June 16th, 2017, 03:08 PM   #3
Math Team
 
MATHEMATICIAN's Avatar
 
Joined: Jul 2013
From: काठमाडौं, नेपाल

Posts: 442
Thanks: 36

Math Focus: Elementary Mathematics
$\displaystyle f(x)=\left \lceil \sqrt{x} \right \rceil^{2}$

for a positive number 'x' if you take the square root of 'x' and again square it will give the same value. If you square a value less than the square root of 'x' it will give lesser value than 'x' and if you square a value greater than the square root of 'x' it will give greater value than 'x'

so, if you square a whole number just greater than the square root of 'x' you will get the desired value.

for example:

if $\displaystyle x = 98 $
$\displaystyle f(x)=\left \lceil \sqrt{98} \right \rceil^{2}$
$\displaystyle f(x)=\left \lceil 9.8994949.......\right \rceil^{2}$
$\displaystyle f(x)=10^{2}$
$\displaystyle \therefore f(x)=100$
MATHEMATICIAN is offline  
June 16th, 2017, 03:11 PM   #4
Newbie
 
Joined: Oct 2015
From: Greece

Posts: 24
Thanks: 0

Thank you guys so much! That was easy but i don't know much about logarithms so this is why i couldn't think about it myself.
babaliaris is offline  
June 16th, 2017, 03:12 PM   #5
Math Team
 
MATHEMATICIAN's Avatar
 
Joined: Jul 2013
From: काठमाडौं, नेपाल

Posts: 442
Thanks: 36

Math Focus: Elementary Mathematics
Seems like I misunderstood the question .......

Last edited by skipjack; June 17th, 2017 at 02:19 AM.
MATHEMATICIAN is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
custom, function



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
guessing the base function of a real function that meets certain requirements vlekje5 Pre-Calculus 11 March 27th, 2017 12:58 PM
Inverting the Riemann Zeta Function with the Mobius Function neelmodi Number Theory 0 February 4th, 2015 10:52 AM
Derivation of tau function, sigma, euler and mobius function msgelyn Number Theory 2 January 12th, 2014 04:13 AM
Find all linear function given a function equals its inverse deSitter Algebra 4 April 10th, 2013 01:17 PM





Copyright © 2017 My Math Forum. All rights reserved.