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Math Help - Logs

  1. #1
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    Logs

    So my teacher has asked me...

    to write ANY log function and answer these questions:
    1. what is the domain?
    2. what is the range?
    3. at what interval is the function negative?
    4. at what interval is the function positive?

    But he didn`t give us any examples so I don`t really know what to do... if someone could provide me with an example on this that would be more then appreciated.


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  2. #2
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    Re: Logs

    for example :

    y=\log_2(x+1)

    1. domain

    x+1>0 \Rightarrow x\in (-1,+\infty)

    2. range

    y \in (-\infty,+\infty)

    3. y<0

    x \in(-1,0)

    4. y>0

    x \in(0,+\infty)
    Last edited by princeps; April 9th 2012 at 11:01 PM.
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  3. #3
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    Re: Logs

    Hello, I'm a new user.

    How can I solve this equation: log 8x-log(1+square root of x)=2? Explain me step by step how do you do it. Thanks.
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  4. #4
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    Re: Logs

    You should have learnt the following:

    log(a)+log(b)=log(ab)

    log(a)-log(b)=log\left(\frac{a}{b}\right)

    log_b a=c \iff b^c=a

    If you're going to be able to apply these (and others) you first need to learn them.

    Also, it's better to start a new thread for a new question.
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  5. #5
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    Re: Logs

    I know that but I'm stuck where I have to write in general form.
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  6. #6
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    Re: Logs

    Well for a start you should apply log(a)-log(b)=log\frac{a}{b}. Post what you get.
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  7. #7
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    Re: Logs

    I get: log 8x/1+square root of x= 2, then I put base 10 on both sides.
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  8. #8
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    Re: Logs

    If I were not using LaTeX I'd use brackets, like this

    log[ 8x / (1+sqrt(x) ) ] = 2

    However LaTeX is easy.. \log\left(\frac{8x}{1+\sqrt{x}}\right)=2

    Yes, if this is base 10 you would then have \frac{8x}{1+\sqrt{x}}=10^2

    Link to LaTeX help to follow..
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  9. #9
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    Re: Logs

    where is LaTex help? and yes I did what you did above, and what next?
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  10. #10
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    Re: Logs

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  11. #11
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    Re: Logs

    How do I use that?
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  12. #12
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    Re: Logs

    How do you use what?
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  13. #13
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    Re: Logs

    The LaTex Tutorial.
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  14. #14
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    Re: Logs

    Click where it says Latex.pdf and have a read.
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  15. #15
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    Re: Logs

    I dont know how to write substracting operations.
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