f4 maths question (10 marks)

Question

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

Answer 1

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

Answer 2

1) 1

3) 0.07918