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    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.
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    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.
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    (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.
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    Let's make the temporary substitution of  y = \log_{10} x ; then:

     \dfrac{1}{3-y} + \dfrac{2}{y-1} = 3 \iff 1(y-1) + 2(3-y) = 3(3-y)(y-1) , and after expanding, it's a quadratic in y.

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

    Hope this helps :smile:
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    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!
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    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 :rolleyes:
 
 
 
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