1. [SOLVED] logarithmic equation

$27^{x}(3x+1)=6$

2. Originally Posted by Waat

I managed to get to that point, have no idea what to do now.

$3x+\log_3 (3x-1)=\log_3 6$

Hi

I am afraid this equation cannot be solved without a calculator.
Are you sure you need to solve it ?
Are you allowed to use a calculator ?

3. Originally Posted by running-gag
Hi

I am afraid this equation cannot be solved without a calculator.
Are you sure you need to solve it ?
Are you allowed to use a calculator ?
Yeah, without a calculator.

4. Originally Posted by Waat

I managed to get to that point, have no idea what to do now.

$3x+\log_3 (3x-1)=\log_3 6$

5. Made a mistake , it(the original equation) should be
$27^{x}(3x+1)=6$

6. Originally Posted by Waat
Made a mistake , it(the original equation) should be
$27^{x}(3x+1)=6$
The first thing I'd do is try a value of x that gives a nice value for 27^x. So try x = 1/3 ....

(There is no formal algebraic way of doing this question, it has to be done in a way like I have suggested above).

7. Originally Posted by mr fantastic
The first thing I'd do is try a value of x that gives a nice value for 27^x. So try x = 1/3 ....

(There is no formal algebraic way of doing this question, it has to be done in a way like I have suggested above).
I've just asked a really smart guy. He suggested using the lambert w function. Thanks for help anyway.

8. Originally Posted by Waat
I've just asked a really smart guy. He suggested using the lambert w function. Thanks for help anyway.
I feel like such a dope suggesting that the solution could be easily found be inspection.

Actually I was going to suggest the Lambert W-function could be used to get a formal algebraic solution but:

1. I didn't think you had the mathematical background to understand this and didn't want to cause confusion.

2. I didn't want to use an elephant gun to kill a fly.

You will find MHF has many threads showing how the Lambert W-function can be used to solve equations eg.

http://www.mathhelpforum.com/math-he...need-help.html

http://www.mathhelpforum.com/math-he...-equation.html

http://www.mathhelpforum.com/math-he...g-ln-x-kx.html

http://www.mathhelpforum.com/math-he...ed-itself.html

You should have no trouble applying the same idea to your question. You will still get x = 1/3 as the answer but at least you'll be able to justify the solution algebraically.