唔識做功課48

Simplify the expression

1. (log x^3 + 3log √y) ÷ (4log(xy) - log y^2)

2. If 1/2 log y = 1+ log x, express y in terms of x.

3 個解答

評分
  • SC147
    Lv 6
    5 年 前
    最佳解答

    1. (log x^3 + 3log √y) ÷ (4log(xy) - log y^2)

    = (log x^3 + log y ^3/2 ) ÷ (log (xy)^4 - log y^2)

    = (log x^3 * y ^3/2) ÷ (log x^4* y^2)

    = log ( x^6/2 * y^3/2) ÷ log ( x^2* y)^2

    = log (x^2 *y)^3/2 ÷ log (x^2 *y)^2

    = 3/2 log (x^2 *y) ÷ 2 log(x^2 *y)

    = 3/2 ÷2

    = 3/4 (Answer)

    2. If 1/2 log y = 1+ log x, express y in terms of x.

    1/2 log y = 1+ log x

    1/2 log y = log 10+ log x

    log y^1/2 = log (10*x)

    y^1/2 = (10*x)

    ( y^1/2)^2 = (10*x)^2

    ∴y = 100 x^2 (Answer)

    2015-02-17 00:31:06 補充:

    希望幫到妳,相信我給妳的答案是正確。

  • 5 年 前

    很有禮貌。

    敬祝各位新年進步!

    ╭∧---∧╮

    │ .✪‿✪ │

    ╰/) ⋈ (\\╯

  • 5 年 前

    thank you so much

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