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Inverse of log function

  1. Sep 30, 2008 #1
    1. The problem statement, all variables and given/known data

    f(x) = log2 x + 3
    2 log2 x − 1
    how do i find the inverse of this? how do i find the range and domain of a log function?

    2. Relevant equations

    f(x) = log2 x + 3
    2 log2 x − 1

    is equal to
    f(x) = log2 x + 3 - log2 (x − 1)2

    D of f(x) = R of f-1(x)

    3. The attempt at a solution

    i tried changing the base but it didnt work...
    Last edited: Oct 1, 2008
  2. jcsd
  3. Sep 30, 2008 #2
    also, is the inverse of

    f(x) = 2x−1 + 3

    log2 (x/3) +1 = y

    f(x) = log2/3(x − 2) − 4

    (2/3)x+4 + 2 = y

    are these correct?
  4. Oct 1, 2008 #3

    Gib Z

    User Avatar
    Homework Helper

    Ok. Your attempt was sadly, incorrect, although similar to something you were probably thinking of:

    [tex]\log_c ( \frac{a}{b} ) = \log_c a - \log_c b[/tex],

    which is not the same as what you tried: [tex] \frac{ \log_c a}{\log_c b} = \log_c a - \log_c b[/tex], which is not true.

    It might help if you let [itex]u= log_2 x[/itex] so that you may view the problem easier. Doing so, solve the equation you have for you, replace the expression in x back in and solve it for x. Then swap your x and f(x), thats your inverse function!

    For your second problem, not quite. Solve it for x first. So First take 3 to the other side,

    [itex]2^{x-1} = f(x) - 3[/itex]. After that, take log_2 of both sides, hopefully you can see the rest. Then just swap x for f(x).

    The last one looks correct, good work =]
  5. Oct 1, 2008 #4


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    Staff Emeritus
    Science Advisor

    Presumably you know that the domain and range of any function of the form loga(x) is {x|x> 0} and all real numbers respectively.

    You also should know that the domain of a rational function is all numbers such that the denominator is not zero.

    Putting those together, the domain of loga(f(x))/loga(g(x)) is all x such that x is positive and g(x) is not 1 (so that log(g(x)) is not 0).
  6. Oct 1, 2008 #5
    so the domain of the 1st one is x=>0 ? because log can never be zero or negative?

    i still cant get the inverse tho...
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