中四log數有5題!!!!

1.
log3 = a,
log5 = b,
log 2 – log27 = log(10/5) – log 3^3
= log10 - log 5 –3 log 3
= 1- b –3a

2 express x in terms of y

a. logx=2logy
log x = log (y^2)
x = y^2

b. log(xy)=2
log (xy) = 2log10
log (xy) = log10^2
xy = 10^2
xy = 100
x = 100/y

c. 1/2 logx=2+log y
log x^1/2 = 2 log10 + log y
log x^1/2 = log10^2 + log y
log x^1/2 = log100 + log y
log x^1/2 = log 100y
x^1/2 = 100y
Square on both sides
x^1/2 = 10000y^2

d. log(4) (x-2y)=3
log(4) (x-2y)=3log10
log(4) (x-2y)= log10^3
log(4) (x-2y)= log1000
(4) (x-2y)= 1000
x – 2y = 250
x = 250 + 2y


2011-02-14 01:39:51 補充：
Correction:
2. d.
If log is to the base of 4, not to the base of 10 as in log [(4)( x - 2y)]
The calculation is different.

log 4 (x - 2y) = 3
4^3 = x -2y
64 = x - 2y
x = 64 + 2y