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    cads2 Posts: 1, Reputation: 1
    New Member

    Nov 16, 2006, 08:18 PM
    logarithmic function
    I need to answer this logarithmic function. Label at least three points on the graph and vertical asymptote. y=3+log5x.
    kyop's Avatar
    kyop Posts: 48, Reputation: 11
    Junior Member

    Nov 16, 2006, 10:04 PM
    Quote Originally Posted by cads2
    I need to answer this logarithmic function. Label at least three points on the graph and vertical asymptote. y=3+log5x.
    Since you are asking for specific points I will assume that you are just starting with graphing log functions. So, you probably could use a little refresher on how logs work. If not, sorry to give you too much information.

    Logarithms are the undoing of exponents. 10^3 = 1000 would be written as
    log (base 10) 1000 = 3.

    Now, since this problem is working in base 10 (when it's not written you just assume base 10), you can actually capitalize on the 5x to make your problem especially easy.

    For instance, what if you were to make x=2? That would create log (base 10) 5(2) or simply log(base 10) 10. This translates to 10^(?) = 10. The question mark is obviously a "1". So, log(base 10)10 = 1.

    Substitute that in to your equation and you get: y = 3+1 or simply y = 4.

    So, you used x=2 to generate y=4. Therefor (2,4) would be one of your points.

    You can use x = 1/5 if you like. Yes, 1/5 isn't exactly a pretty x-value, but it will make y work out very well.

    y = 3 + log 5(1/5)
    y = 3 + log 1
    y = 3 + 0 (since 10^0 = 1) - Let me know if you need instruction on this point
    y = 3

    So, (1/5, 3) is another point.

    The only other point that would work well and still fit on a graph is x=20.
    y = 3 + log 100
    y = 3 + 2
    y = 5

    So, (20, 5) would be the third point.

    As for the asymptote, can you ever find a value for x where 10^x = 0? The answer is no, you can't. So, your vertical asymptote would be the line x = 0.

    I hope this helps. If you need any further explanation, let me know.

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