# Logarithmic Equation

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• May 9th 2010, 08:55 AM
BobBali
Logarithmic Equation
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.
• May 9th 2010, 09:14 AM
Anonymous1
Quote:

Originally Posted by BobBali
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 9th 2010, 09:24 AM
BobBali
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' ?
• May 9th 2010, 10:02 AM
skeeter
Quote:

Originally Posted by BobBali
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 $y = 3\log(2x) - (x-3)$ and look for the real zero.
• May 9th 2010, 10:11 AM
Anonymous1
Quote:

Originally Posted by BobBali
(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.
• May 10th 2010, 01:55 AM
BobBali
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)