急 ! Logarithmic Function 9q6

18.
(a)
log 1.5
= log (3/2)
= log 3 - log 2
= y - x


(b)
log24 (1/6)
= log (1/6) / log 24
= log (2 x 3)^(-1) / log (2^3 x 3)
= -log (2 x 3) / log (2^3 x 3)
= -(log 2 + log 3) / (log 2^3 + log 3)
= -(log 2 + log 3) / (3log 2 + log 3)
= -(x + y)/(3x + y)


(c)
log √(5/27)
= log [10/(2 x 3^3)]^(1/2)
= (1/2) log [10/(2 x 3^3)]
= (1/2)[log 10 - log 2 - log 3^3]
= [log 10 - log 2 - log 3^3]/2
= [log 10 - log 2 - 3log 3]/2
= (1 - x - 3y)/2


*****
19.
(a)
(1/4) log x^3 = 1 + log 5y
log (x^3)^(1/4) = log 10 + log 5y
log x^(3/4) = log 50y
x^(3/4) = 50y
x = (50y)^(4/3)


(b)
log5 (3x - 4y) = 2
log5 (3x - 4y) = 2 log5 5
log5 (3x - 4y) = log5 5^2
log5 (3x - 4y) = log5 25
3x - 4y = 25
3x = 4y + 25
x = (4y + 25)/3

2012-04-02 02:20:28 補充：
To fighting gravity :

你計錯了以下題目：

8.(b) :
log1/log24-log6/24 = [log1 - (log2 + log3)]/(log3 + 3log2) = -(log2 + log3)/(log3 + 2log2)
而不是你寫的 =(1-log2+log3)/(log3+3log2)
原因可能你誤以為 log1 = 1，而且拆錯了括號。

8. (c) :
你只是計至中途，未計得答案。

18a
log1.5
=log(3/2)
=log3-log2
=y-x

18b
=log1/log24-log6/24
=(1-log2+log3)/(log3+3log2)
=(1-x+y)/(y+3x)

18c
log√(5/27)
=log√5-log3√3
=log√5-log3+log√3
=log√5+log√3-log3

19a
(1/4) log x^3 = 1 + log 5y

log (x^3)^(1/4) = log 10 + log 5y
log x^(3/4) = log 10 + log 5y
x^(3/4) = 50y
x = (50y)^(4/3)
19b
log(3x-4y)/log5=2
log(3x-4y)=log25
3x=25+4y
x=(25+4y)/3