Math Help - Logarithmic Equation

1. 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.

2. 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.

3. Urrr..

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' ?

4. 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.

5. 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, I tried to do this at first...

Had to resort to MATLAB.

6. Are you Serious?

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?