natnatwebb
Okay I'm almost there but the answer I'm getting is incorrect.
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natnatwebb
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\[\ln (x)+\ln (x-2)=\ln 8\]
natnatwebb
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then...\[\ln (x)(x-2)=\ln 8\]
natnatwebb
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then...\[\ln (x ^{2}-2x)=\ln 8\]
natnatwebb
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then drop the ln...
\[x^{2}-2x=8\]
gohangoku58
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going good...
RyanL.
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well you e^ both sides. That's how the ln cancel. But then you are left with a quadratic equation
natnatwebb
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split the two,
\[x^{2}=8\]
and
\[-2x=8\]
gohangoku58
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thats incorrect
Jerry123gnzcraft
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true ok ok
gohangoku58
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u need quadratic formula
gohangoku58
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Compare your quadratic equation with \(ax^2+bx+c=0\)
find a,b,c
then the two roots of x are:
\(\huge{x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}}\)
gohangoku58
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x^2-2x-8=0
natnatwebb
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okay gimme a second to work that out.
gohangoku58
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sure.
freewilly922
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*** and need to remember to check for valid values of x.
if you are taking ln(x) and ln(x-2) what can't x be?
RyanL.
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You can always complete the square. That's another way of solving this without the long work of using the quadratic
natnatwebb
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2
natnatwebb
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whats finishing the square? Sounds like a shortcut I was denied...
Jerry123gnzcraft
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granted
gohangoku58
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shortcut only if u have some prsctice.... u wanna learn that ?
freewilly922
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... or just factor? \[x^2-2x-8=0=(x-?)(x+?)\]
Jerry123gnzcraft
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practice some more then use that form
gohangoku58
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factoring is best here..
gohangoku58
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can u factor ?
natnatwebb
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I'll give it a shot! :)
gohangoku58
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sure do :)
Jerry123gnzcraft
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go han!!!! go ku!!!! dominate the problem TEAMWORKKKK
gohangoku58
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? jerry ?
Jerry123gnzcraft
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GO HAN GO KU
RyanL.
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\[x^2−2x−8=0=(x−A)(x+B)\\ A*B=-8\\ A+B=-2\]
Find A and B
natnatwebb
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Almost there....
RyanL.
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You have a system of question where you can simply plug in one equation to another if you can't see it right away. Then solve for the missing variable.
natnatwebb
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its (x-4)(x+2)
gohangoku58
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thats correct :)
gohangoku58
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so what are 2 values of x u got ?
natnatwebb
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ten solving its 4 and -2
RyanL.
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\[(x-4)(x+2)=0\]
natnatwebb
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and -2 would be extraneous
gohangoku58
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but can x be -2 ?? think ....
gohangoku58
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yes, so x is only = ?
natnatwebb
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4?
gohangoku58
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yup, u got it :)
natnatwebb
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HAZUAHH!
natnatwebb
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THanks everyone! I really appreciate it! :)
gohangoku58
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welcome ^_^