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Solve each equation. Round decimal answers to the nearest thousandth.

5(0.10)^x = 4(0.12)^x

  • Math -

    5(0.10)^x = 4(0.12)^x.

    Take log of both sides:
    log5 + xlog(0.10) = log4 + xlog(0.12)0.6990 - x = 0.6021 - 0.9208x,
    -x + 0.9208x = 0.6021 - 0.6990,
    -0.0792x = -0.0969,

    X = -0.0969 / -0.0792 = 1.22.

  • Math -

    CORRECTION:

    Take log of both sides:
    log5 + Xlog(0.10) = log4 + Xlog(0.12),
    0.6990 - X = 0.6021 - 0.9208X,
    -x + 0.9208X = 0.6021- 0.6990,
    -0.0792X = -0.0969,

    X = -0.0969 / -0.0792 = 1.22.

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