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Math Help - Help simplifying basic expression with e

  1. #1
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    Help simplifying basic expression with e

    I have x/4 = lny This simplifies to y=e^(x-4)

    Can someone help me understand the basic inverse properties of ln and e that would make x/(4 x ln)=y simplify to the answer above? Thanks.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Help simplifying basic expression with e

    Use the definition of the logarithm: \ln(x)=y \Leftrightarrow e^{y}=x
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  3. #3
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    Re: Help simplifying basic expression with e

    I'm not sure "simplify" is the right word.

    You should have this property...The following Two statements are identical.

    1) log_{b}(a) = c
    2) b^{c} = a

    For suitable a, b, and c.

    How does this apply to your problem statement?

    Revise: See, SIRON even called it a "Definition". It's not really a "simplify" thing.
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  4. #4
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    Re: Help simplifying basic expression with e

    I understand the two statements and the conversion you guys give, but I don't know how to apply them correctly to this problem.
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    MHF Contributor Siron's Avatar
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    Re: Help simplifying basic expression with e

    You can say: \frac{x}{4}=\ln(y) \Leftrightarrow e^{\frac{x}{4}}=y
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    Re: Help simplifying basic expression with e

    Quote Originally Posted by benny92000 View Post
    Can someone help me understand the basic inverse properties of ln and e that would make x/(4 x ln)=y simplify to the answer above? Thanks.
    The natural log needs an argument and this has none. What is the question in full?
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  7. #7
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    Re: Help simplifying basic expression with e

    I don't remember the exact question. I understand it now. Thanks!
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