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Math Help - Natural Log Question

  1. #1
    Member RedBarchetta's Avatar
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    Natural Log Question

    Can someone show me how this is possible?

    <br />
\ln \left( {\frac{{\sqrt 2  + 1}}<br />
{{\sqrt 2  - 1}}} \right) = 2\ln \left( {\sqrt 2  + 1} \right)<br />

    Thank you.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by RedBarchetta View Post
    Can someone show me how this is possible?

    <br />
\ln \left( {\frac{{\sqrt 2  + 1}}<br />
{{\sqrt 2  - 1}}} \right) = 2\ln \left( {\sqrt 2  + 1} \right)<br />

    Thank you.
    Multiply the inside of the natural log by the conjugate of the denominator:

    <br />
\ln \left( {\frac{{\sqrt 2  + 1}}<br />
{{\sqrt 2  - 1}}}\cdot{\color{red}\frac{\sqrt 2+1}{\sqrt 2+1}} \right)=\ln\left(\frac{(\sqrt 2+1)^2}{2-1}\right)=\ln\left( (\sqrt 2+1)^2\right)=\color{red}2\ln\left(\sqrt 2+1\right)

    Does this make sense?

    --Chris
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  3. #3
    Member RedBarchetta's Avatar
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    ^^Yeah. That makes sense.
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