Question

A confusing math logarithm problem.

Answer 1

\[x^3-x=\log(x+1)\]please guide, don't do it for me, tho...

Answer 2

@tkhunny can you please help?

Answer 3

What do you want to do with it? There is no simple, algebraic, closed-form expression for the solution. How are your numerical methods?

Answer 4

Well, I saw this in my book, and I have to solve for x.

Answer 5

I can guess that zero is a solution, because
0^3 - 0 = log(1)
since log(1) is zero.

Answer 6

No, you don't. It can't be done. Some author is pulling your leg.

Answer 7

Guessing is certainly a valid method, particularly since nothing else will produce anything.

Answer 8

So, there is NO WAY to "solve" it?

Answer 9

I plugged it into wolfram and it gave me a second solution, approximately 1.28 or something like this.

Answer 10

Well, if not, not... thank you for the help:)

Answer 11

No, there are many ways to solve it.
1) Guessing.
2) Various numerical methods.

If it is a Base 10 logarithm, the second solution is between 1.13 and 1.14.
If it is a Base e logarithm, the second solution is between 1.28 and 1.29.

Please specify the base of logarithm functions when it is not ultimately obvious.

Answer 12

For example, after six applications of "Newton's Method", starting with x = 1, we achieve 1.28201560047703.