Register to reply

Sum of the Values of X, Exponential Equation

by wiraimperia
Tags: equation, exponential, logarithm, sum, values
Share this thread:
wiraimperia
#1
Jul6-12, 05:39 AM
P: 9
1. The problem statement, all variables and given/known data
(4x)^(1 + log(base 2) (x)) = 8(x^3)
What is the sum of the values of x that fullfill that equation?
A) 2.5
B) 2.0
C) 1.5
D) 1.0
E) 0.5


2. Relevant equations
Use the exponential equation only and make the lower one (exponented) 1.


3. The attempt at a solution
(4x) = (2 x^(1/2))^2
8(x^3) = (2x)^3
If I insert x = (1/4) to make 4x = 1 it doesn't fulfill the equation..
So does x = (1/2)..
I cannot simplify the exponential equation... Any assistance please?
Phys.Org News Partner Science news on Phys.org
Physicists discuss quantum pigeonhole principle
Giant crater in Russia's far north sparks mystery
NASA Mars spacecraft prepare for close comet flyby
tiny-tim
#2
Jul6-12, 06:20 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,160
hi wiraimperia!

(try using the X2 and X2 buttons just above the Reply box )

for any number n, what is nlog2(x) ?
Simon Bridge
#3
Jul6-12, 07:00 AM
Homework
Sci Advisor
HW Helper
Thanks
Simon Bridge's Avatar
P: 12,447
[tex]4x(4x)^{\log_2x} = 8x^3[/tex]
... how many values of x satisfy the equation?

I'd recheck for x=1/2 ...

wiraimperia
#4
Jul6-12, 10:18 AM
P: 9
Sum of the Values of X, Exponential Equation

I mean if it has 2 solutions, then we are asked X1 + X2, if it has 3, then X1 + X2 + X3, and so on...
ehild
#5
Jul6-12, 11:34 AM
HW Helper
Thanks
P: 10,366
Quote Quote by wiraimperia View Post
I cannot simplify the exponential equation... Any assistance please?
Try to take the logarithm of both sides.

ehild
tiny-tim
#6
Jul6-12, 12:38 PM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,160
for any number m, what is (2m)log2(x) ?
Simon Bridge
#7
Jul7-12, 01:42 AM
Homework
Sci Advisor
HW Helper
Thanks
Simon Bridge's Avatar
P: 12,447
Quote Quote by wiraimperia View Post
I mean if it has 2 solutions, then we are asked X1 + X2, if it has 3, then X1 + X2 + X3, and so on...
Is there any way you can figure out how many solutions it is likely to have?
Have you rechecked if x=1/2 is a solution? Personally I managed it by systematic guesswork using the list of possible solutions ... but I've had practice.

Have you tried any of the other suggestions and hints? They are all good.

Is there a particular method you are supposed to use or can we throw anything we like at the problem? eg. there's always brute-force methods like plotting the curves to get ballpark figures and then using Newton/Raphson ...
Pranav-Arora
#8
Jul7-12, 01:50 AM
P: 3,805
Taking logarithm on both sides with base 2, you get:
[tex](1+log_2 x)log_2(4x)=3+3log_2 x[/tex]

It is easy to solve now.


Register to reply

Related Discussions
Exponential sum equation Calculus 5
Exponential equation Precalculus Mathematics Homework 5
Exponential equation Precalculus Mathematics Homework 7
Converting a log equation to exponential equation Precalculus Mathematics Homework 4
Equation with exponential Precalculus Mathematics Homework 2