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

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

Hello MHF! First time poster here, the following is my problem:

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

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

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

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

By removing logs I ended up with:

$\displaystyle x^3 - x^2 = 10$

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.

2. 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

3. Re: Assignment Logarithmic issue (solved past logs but can't solve last bit)

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?

4. 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.

5. Re: Assignment Logarithmic issue (solved past logs but can't solve last bit)

Thanks kindly!