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Math Help - logs and what not

  1. #1
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    logs and what not

    Solve for x using logs. Give an exact answer.

    35= 400e^(-0.4x)
    Could someone point me in the right direction? Applying the logs to e is what's confusing me...

    and then finding the inverse function of this problem...

    f(t)=77e^(0.2t)

    any help is greatly appreciated
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  2. #2
    Senior Member pacman's Avatar
    Joined
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    35= 400e^(-0.4x)?

    Using logarithm to the base e,

    ln (35) = ln (400) + ln (e^-0.4x)

    ln (35) = ln 20^2 + (-0.4x) ln (e); [where ln e = 1]

    ln (35) = 2 ln (20) - 0.4x

    0.4x = 2 ln (20) - ln (35)

    x = [2 ln (20) - ln (35)]/0.4 = 6.0903
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