{f.4 math} 對數方程

1. logx + log(x + 1) = log6
log[x(x + 1)] = log6
x(x + 1) = 6
x^2 + x - 6 = 0
(x + 3)(x - 2) = 0
x = -3(rejected as log(-3) is undefined) or x = 2.
2. log(x - 1) + log(x + 4) = log84
log[(x - 1)(x + 4)] = log84
(x - 1)(x + 4) = 84
x^2 + 3x - 88 = 0
(x + 11)(x - 8) = 0
x = -11 (rejected) or x = 8.
3. (logx)^2 - log x^2 - 3 = 0
(logx)^2 - 2logx - 3 = 0
[logx - 3][logx + 1] = 0
logx = 3 or -1
x = 1000 or 0.1

1) log x + log (x+1) = log 6

log (x(x+1) = log 6
log x^2+x =l og 6 將兩邊log約左佢
x^2+x = 6
x^2+x-6 = 0
(x+3)(x-2) = 0
so x=-3(捨去)
或x = 2

2) log (x-1) + log (x+4) = log 84

log (x-1)(x+4) = log 84
log x^2+3x-4 = log 84
x^2+3x-4-84 = 0
(x-8)(x+11) = 0
so x=8 或 x=-11(捨去)

3) (log x)^2 - log x^2 - 3 = 0

設logx=y
1) log x + log (x+1) = log 6

log (x(x+1) = log 6
log x^2+x =l og 6 將兩邊log約左佢
x^2+x = 6
x^2+x-6 = 0
(x+3)(x-2) = 0
so x=-3(捨去)
或x = 2

2) log (x-1) + log (x+4) = log 84

log (x-1)(x+4) = log 84
log x^2+3x-4 = log 84
x^2+3x-4-84 = 0
(x-8)(x+11) = 0
so x=8 或 x=-11(捨去)

3) (log x)^2 - log x^2 - 3 = 0

設logx=y
(log x)^2 - 2(log x) - 3 = 0
y^2 - 2y - 3 =0
(y-3)(y+1)=0
y=3 或 y=-1
log x=3 或 log x=-1
x = 10^3 或 x = 0.1

1. logx + log(x + 1) = log6

log[x(x + 1)] = log6

x(x + 1) = 6

x^2 + x - 6 = 0

(x + 3)(x - 2) = 0

x = -3(rejected as log(-3) is undefined) or x = 2.

2. log(x - 1) + log(x + 4) = log84

log[(x - 1)(x + 4)] = log84

(x - 1)(x + 4) = 84

x^2 + 3x - 88 = 0

(x + 11)(x - 8) = 0

x = -11 (rejected) or x = 8.

3. (logx)^2 - log x^2 - 3 = 0

(logx)^2 - 2logx - 3 = 0

[logx - 3][logx + 1] = 0

logx = 3 or -1

x = 1000 or 0.1