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Math Help - Solve Each Log Equation

  1. #1
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    Solve Each Log Equation

    (1) ln e^(-2x) = 8

    (2) log_5 (625) = x
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  2. #2
    MHF Contributor red_dog's Avatar
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    1) \ln e^a=a

    2) \log_5 5^a=a, so try to write 625 as a power of 5.
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  3. #3
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    Tell me...

    I don't understand the rule lne^a = a and how to apply this rule to question 1.
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  4. #4
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by magentarita View Post
    I don't understand the rule lne^a = a and how to apply this rule to question 1.
    The rule is a consequence of the fact that the basic exponential and logarithmic functions are inverses of each other. From what I've seen, it would be best at present if you just memorised it. Understanding migt come in the passing of time.

    Using the rule:

    \ln e^{-2x} = -2x \, ....

    \log_{5} 625 = \log_{5} 5^4 = 4 \, ....
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  5. #5
    Senior Member nikhil's Avatar
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    Quote Originally Posted by magentarita View Post
    I don't understand the rule lne^a = a and how to apply this rule to question 1.
    lne^a=a lne
    now we may prove lne=1 so that you may get
    lne^a =a lne = a
    well lne is actually ln_e(e)
    let ln_e(e)=t
    then e^t=e
    comparing both sides we get t=1
    so ln_e(e)=lne=1 so
    lne^a=a lne =a hence proved
    1) lne^(-2x)=8
    -2xlne=8
    but lne=1 (already proved)
    -2x=8
    x=-4
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  6. #6
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    Thanks to all...

    Thank you all, especially nikhil for that simple explanation.
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