f4 maths question (10 marks)

🎓 學業台小學及中學教育

Man

2007-10-31 2:28 am

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1:

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

回答 (2)

Gabriella Montez

2007-10-31 4:09 am

✔ 最佳答案

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.)

參考: My Maths Knowledge

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[匿名]

2007-11-04 3:07 am

1) 1
3) 0.07918

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