Logarithmic functions

  1. y = logx 4

    identify the domain and range

    state whether the function is increasing or decreasing, and identify the vertical asympotote, teh x-intercept and the value of x at y = 1

    I need some help!

    thank you in advance!
     
  2. jcsd
  3. mathman

    mathman 6,566
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    Gold Member

    The 4 in your expression appears to be hanging out in space. It would be helpful if you could write the equation more clearly.
     
  4. dextercioby

    dextercioby 12,314
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    So your function is:
    [tex] y(x)=\log_{x} 4 [/tex]

    Can you determine the domain and range...??

    Discuss the sign of its derivative...


    Daniel.

    P.S.Can u solve the equation y(x*)=1??Find x*...
     
  5. HallsofIvy

    HallsofIvy 40,663
    Staff Emeritus
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    I believe that loga(x) is only defined for a> 0. Does that help.
     
  6. Zurtex

    Zurtex 1,123
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    Also I don't think that loga(x) is defined for a=1.
     
  7. dextercioby

    dextercioby 12,314
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    Write
    [tex] y(x)=\frac{\ln 4}{\ln x} [/tex]

    Cau u see now what is the range??What about the domain?

    Daniel.
     
  8. See I thought x was 2??
     
  9. dextercioby

    dextercioby 12,314
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    What "2"??Where did u pick it out???You mean the solution to the equation
    [tex] \frac{\ln 4}{\ln x} =1 [/tex]

    I hope you're only kidding...

    Daniel.
     
  10. no, i'm kidding. this problem might as well be in chinese for all i understand of it
     
  11. *** NOT kidding
     
  12. dextercioby

    dextercioby 12,314
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    Write it like that
    [tex]\ln 4=\ln x [/tex]

    Use the fact that logaritm is a surjective function...

    Daniel.
     
  13. i'm sorry i'm not trying to be difficult i just completely dont understand what you are talking about.
     
  14. dextercioby

    dextercioby 12,314
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    Okay.Do you know the relation between the exponential and the natural logarithm???If so,apply exponential on both sides of the last equation and tell me what u get.

    Daniel.
     
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