Exponential and log functions

e^x-e^(-x)=5
e^x- 1/(e^-x)=5
e^2x -1=5e^x
e^2x - 5e^x -1=0

e^x= -(-5)±√[(-5)^2-4(1)(-1)] / 2(1)
=5±√26 / 2
e^x= (5+√29) / 2 or (5-√29) / 2 (rej.) <-------√29 > 5 => 5-√29 < 0 5可以ln佢
ln e^x=ln[(5+√29)/2]
x=ln(5+√29)-ln 2
=1.65 //
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e^x+e^(-x)=3
e^x+ 1/(e^-x)=3
e^2x + 1=3e^x
e^2x - 3e^x + 1=0

e^x=-(-3)±√[(-3)^2-4(1)(1)] / 2(1)
=3±√5 / 2
e^x =3+√5 / 2 or 3-√5 / 2
ln e^x=ln[3+√5 / 2] or ln[3-√5 / 2]
x=ln(3+√5)-ln 2 or ln(3-√5)-ln 2
=0.96 or -0.96 #
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ln(x^2)+ln(2x^4)=16
2ln x+ln 2+4ln x=16
6ln x=16-ln 2
ln x=(16-ln 2)/6
x=e^[(16-ln 2)/6]
=12.82 //
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6^(-x)=20
log [6^(-x)]=log 20
-x log 6 = log 20
x= -log 20 / log 6
=-1.67 //
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你要寫返corr.to 3sig.fig 果d

2012-10-02 10:58:21 補充：
我係當晒你5識打次方(^)果d位係次方
記住5好照抄(^)上去

a)
ex - e-x =5
x(e-1)-e=5
x=(5+e)/(e-1)

b)
ex+e-x =3
x(e-1)+e=3
x=(3-e)/(e-1)

c)
in( x2) + in(2x4) =16
In(2x^6)=16
6In(2x)=16
2x=e^(8/3)
x=[e^(8/3)]/2

d)
6-x =20
x=-14