1. I am asked to find the roots of this function:

ln(x^3 + 1) = sin(2x) + 5

I have completely forgotten how to do this as its been awhile since high school Can anyone please help?

Thanks in advance

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- Jul 8th 2010, 03:11 AMGameTheoryI need help solving for x
1. I am asked to find the roots of this function:

ln(x^3 + 1) = sin(2x) + 5

I have completely forgotten how to do this as its been awhile since high school Can anyone please help?

Thanks in advance - Jul 8th 2010, 03:13 AMAckbeet
That one's nasty. I don't know if it's possible to find the root of that analytically. You might have to use a numerical method or hand it off to a computer.

- Jul 8th 2010, 05:06 AMmr fantastic
- Jul 8th 2010, 09:36 AMGameTheory
The teacher asked me to find the root. You can use analytically, numerically or graphically. Judging from the posts I am assuming that an analytical way is pretty much impossible and therefore I can just use my graphing calculator.

Thanks for confirming - Jul 8th 2010, 09:43 AMAckbeet
Looks to be about 3 solutions. Make sure you know to what precision you need to find the solutions!

- Jul 8th 2010, 09:49 AMAlso sprach Zarathustra
First you need ask yourself is there any roots?

You can prove the existence of roots by some theorems...

(There 3 roots...) - Jul 8th 2010, 09:53 AMAckbeet
Reply to AsZ: Given that this post is in the pre-calculus forum, I doubt if the Intermediate Value Theorem is required, or even that it is required to prove the existence of roots. Certainly, proving existence isn't a bad idea - it could save loads of time, especially if there aren't any...

- Jul 8th 2010, 02:57 PMGameTheory
Using my graphing calculator, i was only able to find 2 roots at: x = 4.8431455 and x = 7.2402863. I wonder where you guys are getting this third root from?

- Jul 8th 2010, 03:12 PMpickslides
How many times did the two functions intersect when you graphed them?

- Jul 8th 2010, 03:14 PMAlso sprach Zarathustra
Between them x=6.66...