# Assignment Logarithmic issue (solved past logs but can't solve last bit)

• Dec 11th 2012, 11:26 AM
Luponius
Assignment Logarithmic issue (solved past logs but can't solve last bit)
Hello MHF! First time poster here, the following is my problem:

$2 log(x) + log(x-1) = 1$

I solved the above by grouping the logs together, resulting in the below:

$log[x^2(x-1)] = 1$

$log[x^3-x^2] = 1$

By removing logs I ended up with:

$x^3 - x^2 = 10$

I simply have no idea how to solve this (it's probably simpler than I might imagine) but the x cubed is confusing me and I cannot find anything I can pull out in common that lets me solve with with an answer of 10 for both brackets or whatever.

Any help is appreciated on the matter.
• Dec 11th 2012, 12:56 PM
OllieC
Re: Assignment Logarithmic issue (solved past logs but can't solve last bit)
Since this equation doesn't have any rational solutions there are a number of different ways of finding the solution for x. Here are some suggestions:
Interval Bisection
Cubic Formula (not so common but takes a form similar to the Quadratic Formula)
Newton-Raphson method

In any case this equation cannot be solved analytically but we can see that a solution exists between 2 < x < 3. Hope this has given you some ideas
• Dec 11th 2012, 01:11 PM
Luponius
Re: Assignment Logarithmic issue (solved past logs but can't solve last bit)
Quote:

Originally Posted by OllieC
Since this equation doesn't have any rational solutions there are a number of different ways of finding the solution for x. Here are some suggestions:
Interval Bisection
Cubic Formula (not so common but takes a form similar to the Quadratic Formula)
Newton-Raphson method

In any case this equation cannot be solved analytically but we can see that a solution exists between 2 < x < 3. Hope this has given you some ideas

I do recall something along the lines of a solution involving a range, but I can't really figure out the proper method to do so, could you please explain in a little more detail? :)

Edit: Does it by any chance involve testing several numbers replacing x and figure out which ones provides a result closest to 0?
• Dec 11th 2012, 02:39 PM
Prove It
Re: Assignment Logarithmic issue (solved past logs but can't solve last bit)
The Bisection Method is the easiest to apply. Decide a region which your solution lies in, halve it, then see which half the solution lies in and repeat the process until you have your desired accuracy.
• Dec 12th 2012, 05:51 AM
Luponius
Re: Assignment Logarithmic issue (solved past logs but can't solve last bit)
Thanks kindly!

:)