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    Hello

    Please help with the following questions and apologies for not using latex:

    Solving for x:

    1. e^4x - e^x=0 (I got 0)

    2. log(base3)x - 4log(base x)3 + 3 = 0

    For the second I brought it down to log(base3)27x = 4/(log(base3)x). Not sure if it's correct up to there.


    Thanks in advance
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    1. Fine. (Why?)
    2. Leave it as log x + 3 = 4/log x. Let t = log x; now you have t + 3 = 4/t. Do you know how to solve this for t? (Try multiplying through by t first.)
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    (Original post by azamally)
    Hello

    Please help with the following questions and apologies for not using latex:

    Solving for x:

    1. e^4x - e^x=0 (I got 0)

    2. log(base3)x - 4log(base x)3 + 3 = 0

    For the second I brought it down to log(base3)27x = 4/(log(base3)x). Not sure if it's correct up to there.


    Thanks in advance


    By inspection I think it is fairly obvious that x=3
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    (Original post by steve2005)
    I think it is fairly obvious
    I see. Why is it fairly obvious that there aren't any other solutions?
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    (Original post by generalebriety)
    I see. Why is it fairly obvious that there aren't any other solutions?
    It is obvious that one of the solutions is x=3 I have not said anything about other possible solutions.

    Incidentally in your earlier post you have suggested replacing log(base3) x and log(base x) 3 with t. Note they are different bases.
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    (Original post by steve2005)
    It is obvious that one of the solutions is x=3 I have not said anything about other possible solutions.

    Incidentally in your earlier post you have suggested replacing log(base3) x and log(base x) 3 with t. Note they are different bases.
    No I haven't: logx(3) = 1/log3(x). All of the logarithms in my first post are to the base 3.
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    (Original post by generalebriety)
    No I haven't: logx(3) = 1/log3(x). All of the logarithms in my first post are to the base 3.
    Sorry I made a mistake in reading your post.

    I have two values for x

 
 
 
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