Logarithmic Equation

May 2010
78
6
Tanzania
Hello,

Need help with solving the following log equation:

3Log(2x) = x-3

I have tried every possible method using log principles, but i am not getting the same answer as that when i use a GDC to look for the intersects. Please help.
 
Last edited:
Nov 2009
517
130
Big Red, NY
Hello,

Need help with solving the following log equation:

3Log(2x) = x-3

I have tried very possible method using log principles, but i am not getting the same answer as that when i use a GDC to look for the intersects. Please help.
Code:
>> syms x;
>> solve('3*log(2*x) = x-3',x)
 
ans =
 
1/(2*exp(1)*exp(lambertw(0, -1/(6*exp(1)))))

W = LAMBERTW(X) is the solution to w*exp(w) = x.
W = LAMBERTW(K,X) is the K-th branch of this multi-valued function.
 
May 2010
78
6
Tanzania
Urrr..

(Crying) I was hoping a detailed step-by-step method was going to be shown. I want to know how we get the answer to 'x' ?
 

skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
I was hoping a detailed step-by-step method was going to be shown. I want to know how we get the answer to 'x' ?
sorry you're disappointed, but the fact is that you'll not be able to solve this equation using elementary algebraic techniques.

the previous response shows a computer generated solution using the Lambert W function.

my advice to you is to get out your calculator and solve it.

graph \(\displaystyle y = 3\log(2x) - (x-3)\) and look for the real zero.
 
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Nov 2009
517
130
Big Red, NY
(Crying) I was hoping a detailed step-by-step method was going to be shown. I want to know how we get the answer to 'x' ?
Sorry, I tried to do this at first...

Had to resort to MATLAB.
 
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May 2010
78
6
Tanzania
Are you Serious?

(Surprised) I cant solve this equation by hand..?! Oh, man... Yes, when i punched it originally into my GDC and looked for the intercept i got x = 6.3 , which checks out when i replace x in the equation. But, i was under the impression it could be solved by hand, apart from taking x/y values and plotting on a graph-paper by hand and looking for the intercepts... How did the Math-Gurus do it 30years ago?? They just graphed it by hand? (Surprised)