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Math Help - Simplify log ad graph exponential

  1. #1
    Junior Member
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    Simplify log ad graph exponential

    Simplify \log a^3 - \log a^2

    I'm not sure if this is right but is it either:

    a) = 3\log_{10} a - 2\log_{10} a
    =\log_{10} a (3-2)
    =\log_{10} a {1}
    a=0

    OR

    b) \log a^3 - \log a^2
    =\log_{10} \frac{a^3}{a^2}
    =\log_{10} a

    ???

    To graph y=e^x
    -1 \leq x\leq 3
    Is it just the exact same as a normal y=e^x but asymptotic at x=-1 and x=3?

    How can I find the gradient of the tangent at (0,1)?
    Last edited by nerdzor; May 16th 2009 at 10:13 PM.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by nerdzor View Post
    Simplify \log a^3 - \log a^2

    I'm not sure if this is right but is it either:

    a) = 3\log_{10} a - 2\log_{10} a
    =\log_{10} a (3-2)
    =\log_{10} a {1}
    a=0

    OR

    b) \log a^3 - \log a^2
    =\log_{10} \frac{a^3}{a^2}
    =\log_{10} a
    b is right .
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  3. #3
    Newbie Singaporean's Avatar
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    b is right
    because from your method A

    if you substitute log a = b
    it would be 3b-2b = b = log a
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