logarithms

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1. if P(t)=3e^2t, for what value does P(t)= 2P(2)

2. Find all x for which the square root of log (x)= log square root of x

thanks!!

  • logarithms -

    1. If P(t) =3P(2)
    then 3e^(2t) = 2(3e^(4t)
    e^(2t) = 2 (e^2t)^2
    let e^2t = y
    y = 2y^2
    2y^2 - y = 0
    y(2y -1) = 0
    y = 0 or y = 1/2

    e^2t = 0 ---> no solution
    or
    e^2t = 1/2
    ln (e^2t) = ln (1/2) = ln1 - ln2 = -ln2
    2t = -ln2
    t = (-1/2)ln 2

    2. √(log(x)) = log (√x) = log x^(1/2) = (1/2) logx
    let logx = y
    √ y = (1/2)y
    y = (1/4)y^2
    4y = y^2
    y^2 - 4y = 0
    y (y - 4) = 0
    y = 0 or y = 4

    logx = 0 or logx = 4
    x = 10^0 = 1 OR x = 10^4 = 10000

  • logarithms -

    My error for #1, see "bobpursley's" answer
    http://www.jiskha.com/display.cgi?id=1355365995

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