F4 Maths

FACT:
log a + log b = log(ab)
log a - log b = log(a/b)

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Q1.

log(x+3) + log (x+12) =1
log [(x+3)(x+12)] =1
x²+15 +36 = 10
x²+15x+26 =0
x = -13(rejected, ∵(x+12)< 0 and (x+3)< 0 )
or x= -2
hence, x = -2
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Q2

log (x+4) + log(x-4) = log 9
log (x²-16) = log 9
x²-16 = 9
x² =25
x= -5 (rejected since (x+4)< 0 and (x-4)<0 )
or x = 5
hence x= 5
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Q3

log(x² - 9) - log (x-5) = log (2x-1)

if this eqt. has solution
x must be smaller than 1/2 due to the term log(2x-1)
however, due to the term log(x - 5), x must be greater than 5
this is contradiction
so this equation has no solution
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2012-05-26 15:09:33 補充：
a number (log K) is valid if and only if K >0

2012-05-26 21:34:47 補充：
Q3 更正:

log(x² - 9) - log (x-5) = log (2x-1)
log (x²-9) = log (2x²-11x+5)
x² -11x+14 = 0
x= [11±(√65)]/2 = 1.47 or 9.53
however, when x = 1.47, (x²-9) <0
so the ans should be [11+(√65)]/2 = 9.53

to wy:
Alex failed Orz

wy,

why you answere this kind of things?

Alex did a great job.