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# Help with logs problem watch

1. Hi guys, I would appreciate any help on a logs problem. I just dont know where to start. Its probably really easy, but my heads just not in it at the moment.

1/(3 - log(x)) + 2/(log(x) - 1) = 3

find all solutions.

note: logs are to the base 10.

Any hints would be great so I can try and handle it myself but if I dont get it eventually i'll ask for an answer.

Cheers.
2. ok i got an answer for this eventually, but i don't know if i've done it in a way which has caused me to miss other solutions (if there are indeed other solutions)

i got x = 100. If anyone can confirm thats the right one and only answer I was really appreciated it.
3. (Original post by RocketTown)
ok i got an answer for this eventually, but i don't know if i've done it in a way which has caused me to miss other solutions (if there are indeed other solutions)

i got x = 100. If anyone can confirm thats the right one and only answer I was really appreciated it.
That's one solution. There is another, not as well rounded.
4. Let's make the temporary substitution of ; then:

, and after expanding, it's a quadratic in .

Indeed x = 100 is one answer, but there is also another.

Hope this helps
5. Damn it! In the time it took me to scribble out the question once I'd read it, two answers have appeared! This always happens!
6. cheers guys. The reason I didn't get it was a fundamental error in my working at the beginning that i'm far too embarassed to state. I'm sure it will never happen again

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Updated: October 9, 2009
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