How to tackle ln(x-2)-ln(x+2)=2?
回答 (7)
2009-05-05 12:21 pm
✔ 最佳答案
ln(x-2)-ln(x+2)=2In [(x-2)/(x+2)] = In(e^2)
(x-2)/(x+2) = e^2
x-2 = x(e^2) + 2(e^2)
x[(e^2) - 1] = -2[1 + (e^2)]
x = 2[1 + (e^2)] / [1 - (e^2)]
2009-05-05 7:24 pm
good old ln's!
ln x - ln y = ln x/y
so
ln(x-2)-ln(x+2)
is the same as
ln(x-2)/(x+2) = 2
the e button or exponential is the opposite of ln, so
e^[ln(x-2)/(x+2)] = e^2
(x-2)/(x+2) = e^2
(x-2) = e^2(x+2)
x-2 = 7.39x + 14.77
x= 7.39x +16.77
6.39x=16.77
x= 2.62
to 2.dp
ln x - ln y = ln x/y
so
ln(x-2)-ln(x+2)
is the same as
ln(x-2)/(x+2) = 2
the e button or exponential is the opposite of ln, so
e^[ln(x-2)/(x+2)] = e^2
(x-2)/(x+2) = e^2
(x-2) = e^2(x+2)
x-2 = 7.39x + 14.77
x= 7.39x +16.77
6.39x=16.77
x= 2.62
to 2.dp
參考: A level maths student
2009-05-05 7:22 pm
lnA - lnB = ln(A/B)
therefore
for the eq above
ln[ (x-2)/(x+2) ] = 2
= (x-2)/(x+2) = exp(2)
you can subsequently get x with simple algebra.
therefore
for the eq above
ln[ (x-2)/(x+2) ] = 2
= (x-2)/(x+2) = exp(2)
you can subsequently get x with simple algebra.
2009-05-05 7:21 pm
ln(x - 2) - ln(x + 2) = 2
ln[(x - 2)/(x + 2)] = 2
(x - 2)/(x + 2) = e^2
x - 2 = e^2(x + 2)
x - 2 = e^2(x) + 2e^2
x - e^2(x) = 2 + 2e^2
x(1 - e^2) = 2(1 + e^2)
x = [2(1 + e^2)]/[(1 + e)(1 - e)]
ln[(x - 2)/(x + 2)] = 2
(x - 2)/(x + 2) = e^2
x - 2 = e^2(x + 2)
x - 2 = e^2(x) + 2e^2
x - e^2(x) = 2 + 2e^2
x(1 - e^2) = 2(1 + e^2)
x = [2(1 + e^2)]/[(1 + e)(1 - e)]
2009-05-05 7:18 pm
ln(a) - ln(b) = ln(a/b)
ln( (x-2) / (x+2) ) = 2
e^2 = (x-2) / (x + 2)
e^2 * (x + 2) = x - 2
e^2 * x + 2 * e^2 = x - 2
e^2 * x - x = -2 - 2 * e^2
x * (e^2 - 1) = -2 - 2 * e^2
x = -2 * (1 + e^2) / (e^2 - 1)
Plug that into your calculator
ln( (x-2) / (x+2) ) = 2
e^2 = (x-2) / (x + 2)
e^2 * (x + 2) = x - 2
e^2 * x + 2 * e^2 = x - 2
e^2 * x - x = -2 - 2 * e^2
x * (e^2 - 1) = -2 - 2 * e^2
x = -2 * (1 + e^2) / (e^2 - 1)
Plug that into your calculator
2009-05-05 7:16 pm
Starting point..
ln(x-2)-ln(x+2)=2
ln((x-2)/(x+2))=2
(x-2)/(x+2) = e^2
and then its simple algebra..!
ln(x-2)-ln(x+2)=2
ln((x-2)/(x+2))=2
(x-2)/(x+2) = e^2
and then its simple algebra..!
2009-05-05 7:16 pm
Tackle? You solve the equation or tackle them?
Use laws of logarithm ( I assume you know them) if you want to solve it. For tackling, consult some one else..
Use laws of logarithm ( I assume you know them) if you want to solve it. For tackling, consult some one else..
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