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Math Help - Logarithm exact value help

  1. #1
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    Logarithm exact value help

    The instructions say that, without a calculator, I have to find the exact value of each. I don't know how to do it at all, and no the last one is not a mistake. That;s what my book says exactly. I know it is odd.

    ln √(e)

    ln(e)^3

    log√(2) 4
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  2. #2
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    Quote Originally Posted by wallflower View Post
    The instructions say that, without a calculator, I have to find the exact value of each. I don't know how to do it at all, and no the last one is not a mistake. That;s what my book says exactly. I know it is odd.

    ln √(e)

    ln(e)^3

    log√(2) 4
     <br />
\ln(\sqrt{e}) = \ln(e)^{\frac{1}{2}} = \frac{1}{2} \ln(e) = \frac{1}{2}\times 1 = \frac{1}{2}<br />

    Use this example to finish the rest.
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  3. #3
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    Thank you! I understand that! The only one I'm having trouble with are teh few that are like this one: log√(2) 4
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  4. #4
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    Quote Originally Posted by wallflower View Post
    Thank you! I understand that! The only one I'm having trouble with are teh few that are like this one: log√(2) 4
    That's very ambiguous.

    Do you mean

    log_{\sqrt2}(4) or log(\sqrt{2^4}).
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  5. #5
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    Oh. I'm sorry! I mean log (√2) 4 with two being the base and 4 being completely outside. Basically the first one you posted
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  6. #6
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    Quote Originally Posted by wallflower View Post
    Oh. I'm sorry! I mean log (√2) 4 with two being the base and 4 being completely outside. Basically the first one you posted
    Okiedoke, for that one I'd use the change of base rule. I'm using log 2 as both numbers are powers of 2 but any base that is greater than 1 works

    log_{\sqrt2}(4) = \frac{log_2(4)}{log(\sqrt2)} = \frac{log_2(2^2)}{log_2(2^{1/2})} = \frac{2}{\frac{1}{2}} = 4
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