moongazer
Find the value of x and y that will satisfy the system



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moongazer
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e^x  y = 2
e^x + y = 1

Matrix65
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is xy and x+y both exponents

sauravshakya
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dw:1349690570593:dw

sauravshakya
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Is that the question?

Matrix65
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introduce In both sides

sauravshakya
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If that is the question then it has no real roots.

moongazer
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how do I solve it?

moongazer
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(e^x)  y = 2
(e^x) + y = 1

moongazer
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sorry for the late reply

sauravshakya
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Then Add equation one and two ........

prawal
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i think no real solution...
u might get5 imaginary....

hartnn
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still e^x = 1/2 has no real solution for x

sauravshakya
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Yes still no real solution

hartnn
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y comes out to be 3/2

hartnn
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u have choices/options ?

sauravshakya
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But that will not be true.

moongazer
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I don't have

FaisalAyaz
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imaginary solution is how?

sauravshakya
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dw:1349691346340:dw

sauravshakya
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dw:1349691384296:dw

moongazer
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that's also what I got


FaisalAyaz
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ok

moongazer
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Isn't it that e^(ln 1/2) =1/2 ?

moongazer
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@hartnn @sauravshakya

hartnn
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yes, thats correct but y did u caculate that ?

moongazer
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nope

hartnn
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i meant yes, thats correct but why did u caculate that ?

prawal
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e^(ln 1/2) =1/2 this is hell wrong... !!
the equation is not defined...

moongazer
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to find y

moongazer
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I got y=3/2

hartnn
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yes, there are no real solutions to this.....

prawal
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impossible man..

moongazer
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What should I write on my paper?

hartnn
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i think u just write e^x=1/2, y =3/2 and leave it

prawal
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u can do the above thing or write no real solution...

hartnn
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*and write no real solution

moongazer
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I think I got the answer

jhonyy9
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ln of a negativ number  how it is possible ?  little up check it please !!!

jhonyy9
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@hartnn ,@sauravshakya

moongazer
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I got x = ln 1
and y = 1

jhonyy9
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@sauravshakya

moongazer
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I think that is the answer

jhonyy9
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check where is defined the logarithm funvtion please

jhonyy9
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function  sorry

moongazer
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I forgot to add e^x

jhonyy9
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e^x  y = 2
e^x + y = 1

hartnn
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ln(1), 1 does not satisfy 2nd equation
ln(1) is imaginary = i\(\pi\)

jhonyy9
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ln(1) how do you mean this ?

moongazer
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it should be ln 1/2 =x
and 3/2=y

jhonyy9
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when by definition logb X so x need being allways positiv

hartnn
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\(e^{i\pi}=1\)
by euler's relation

jhonyy9
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e^x  y = 2
e^x + y = 1
so and for these equations ?

hartnn
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but if x is imaginary, y must be imaginary also, right ?

jhonyy9
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but in this case i think that is very simple
us ln to both sides for every two equations and will get the right answers

moongazer
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when you substitute x with ln 1/2
it will be
e^(ln 1/2)  y = 2
then
1/2y=2
y=3/2

moongazer
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I think my teacher doesn't need to know the decimal value of x.

hartnn
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ok, then write that....

moongazer
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ok, thanks for the answers :)

moongazer
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why is it ln (negative number) is undefined?

jhonyy9
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by domain definition of logarithms

jhonyy9
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you have learned it sure  i think ,yes ?

moongazer
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ohh yes

moongazer
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because of the graph

jhonyy9
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good so than all is understood it right
good luck
bye

moongazer
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Thanks :)
do you know how to decompose a function?

jhonyy9
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how do you think it ?

moongazer
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partial fractions the one with cases.
I got an odd looking expression

moongazer
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i'll post it