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Solve the exponential equation algebraically
5^(-t/2) = 0.20

  • Precal -

    take log on both sides,
    solve for t
    -t/2 = log(0.20)/log(5)

    t=-2log(0.20)/log(5)...isolate t
    =log(1/0.04)/log(5)...absorb -2 into log(0.2)
    =log(25)/log(5)... evaluate reciprocal
    =2... laws of logarithm, 25=5²

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