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March 25, 2017

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Find the EXACT solution to
e^(1-x) = 4^x

You must use logs, not just a calculator.

  • math - natural logs - ,

    take ln of both sides

    ln( e^(1-x) = ln (4^x)
    (1-x)lne = x(ln4)
    1-x = xln4
    xln4 + x = 1
    x(ln4 + 1) = 1
    x = 1/(ln4 + 1)
    = appr. .419

    check
    LS = e^.581 = 1.7877
    RS = 4^.416 = 1.7877 (not bad)

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