f4 maths question (10 marks)

1) if 9 ^ (1/h) = 11 ^ (1/k) = 99 , where h and k isn't equal to 0, determine the value of h + k without finding thhe values of h and k.

2) if x^ (1/4) + x ^(-1/4) = 4, find the values of the following expressions.

a) 開方x + (1/開方x)

b) x + (1/x)

Thanks.

更新:

3) Given log2= 0.301030 and log 3= 0.477121, find to 5 places of decimals log 1.2

2 個解答

評分
  • 1 十年前
    最愛解答

    1) 9^(1/h)=99 (given)

    log9^(1/h)=log99

    (1/h)log9=log99

    h=log9/log99---(1)

    &

    11^(1/k)=99

    log11^(1/k)=log99

    (1/k)log11=log99

    k=log11/log99---(2)

    (1)+(2): h+k=log9/log99+log11/log99

    =(log9+log11)/log99

    =log99/log99

    = 1

    2a)x^(1/4)+x^(-1/4)=4

    x^(1/2)+2+x^(-1/2)=16

    x^(1/2)+x^(-1/2)=14

    b)x+2+x^-1=196

    x+1/x=194

    3)log1.2=log3+log0.4

    =log3+log4-log10

    =log3+2log2-1

    =0.477121+2(0.301030)-1

    =0.07918(cor. to 5 d.p.)

    資料來源: My Maths Knowledge
  • 匿名
    1 十年前

    1) 1

    3) 0.07918

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