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Math Help - How would I graph this Logarithmic function?

  1. #1
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    How would I graph this Logarithmic function?

    \log_{8}(x) + 4

    It's just tricky to input it in my calculator
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  2. #2
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    Your calculator most likely has the button 'log' implying base 10 or 'ln' implying base e. Here is a property that will help you graph logarithmic functions with different bases:

    \log_{a} (b) = \frac{\log_{c} b}{\log_{c}a} where c can be any number.

    Since your calculator probably deals with base 10 and e, those are the values you will use for c, i.e.:

    \log_{8} (x) + 4 \: \: = \: \: \frac{\log(x)}{\log(8)} + 4 \: \: = \: \: \frac{\ln(x)}{\ln(8)} + 4
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mankvill View Post
    \log_{8}(x) + 4

    It's just tricky to input it in my calculator
    if drawing by hand is what you have to do, here's what you need to know

    ALL log graphs of the form y = \log_a x (a > 1) look like the one below. they all pass through the point (1,0), and are asymptotic to the y-axis, and have domain (0, \infty).

    with your graph, you are shifting the log up by 4 units (standard transformation rule when you add a positive constant).

    now, this shift may affect the intercepts. in this case, it affects the x-intercept only. no worries, you can calculate the new intercept.

    for the x-intercept, set y = 0 in your function and solve for x. then just draw a curve that looks like the one below, but instead of passing through (1,0), it passes through the new x-intercept you found.
    Attached Thumbnails Attached Thumbnails How would I graph this Logarithmic function?-log.jpg  
    Last edited by Jhevon; July 7th 2008 at 10:54 PM. Reason: Thanks, Earboth!
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    Quote Originally Posted by Jhevon View Post
    if drawing by hand is what you have to do, here's what you need to know

    ALL log graphs of the form y = \log_a x look like the one below.

    ...
    I don't want to pick at you but the graphs are only similar to your's if a > 1.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by earboth View Post
    I don't want to pick at you but the graphs are only similar to your's if a > 1.
    i assumed that went without saying. i always assume a > 1, you don't see logs with bases less than 1 everyday. i will mention that though. thanks for looking out.
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