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Math Help - Logarithmic functions?

  1. #1
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    Logarithmic functions?

    Graph each equation or inequality

    1.y= log 5(x-1) This is what I did
    y+1= log 5 x
    5^y+1=x Would this be right of setting up the graph so that if y=0 x=5?

    2. y=2 log 2 x I am slightly confused on how to start this
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  2. #2
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    Quote Originally Posted by homeylova223 View Post
    Graph each equation or inequality

    1.y= log 5(x-1) This is what I did
    y+1= log 5 x
    5^y+1=x Would this be right of setting up the graph so that if y=0 x=5?

    2. y=2 log 2 x I am slightly confused on how to start this
    I just want to be clear about your notation do you mean

    y=\log_{5}(x-1) \text{ or } y=\log_{5}(x)-1
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  3. #3
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    I mean the former the one where both x and negative one are in the parenthesis.
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    First you can graph in the method that you started above but you don't have to.

    y=\log_{5}(x-1) \iff 5^y=x-1 \iff x=5^y+1

    You can then pick y values to make a table. Note that the x values get large really quickly.

    Or you can make the table directly from the function. First we know that the log of zero is undefined so when

    x-1=0 \iff x=1

    so there is a vertical asymptote when x=1.

    Also you should know that

    \log_{a}(1)=0

    for any

    a > 0, \quad  a \ne 1

    Now we can just pick powers of the bases to get

    \log_{5}\left(5^{n} \right)=n

    can you finish from here?
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  5. #5
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    For my second question

    y=2 log 2 x Would I do this

    2^y=2x Then would I just divide by 2?
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  6. #6
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    Quote Originally Posted by homeylova223 View Post
    For my second question

    y=2 log 2 x Would I do this

    2^y=2x Then would I just divide by 2?
    if you meant ...

    y = 2\log_2{x}

    then,

    2^y = x^2
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