donovan11
Solve the logarithmic equation for . Please round the answer to four decimal places, if necessary.
ln(x-4)+ln(x+5)=1
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donovan11
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Reason I'm confused is because unlike log, in ln the exponential form is e^y=x and I'm having trouble solving the rest
amistre64
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ln(a) + ln(b) = ln(ab)
donovan11
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That's x^2+x-20?
amistre64
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yep.
now, ln(0) = 1 because e^0 = 1
myininaya
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and also any number to the 0 power except 0 is 1
amistre64
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your equation is really:
x^2 +x - 20 = 0
myininaya
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wait!
amistre64
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or
(x-4) (x+5) = 0
myininaya
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e^1=e
myininaya
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we have (x-4)(x+5)=e
amistre64
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lol..... maybe it does, and maybe it doesnt :)
beens
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yes myininaya
myininaya
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if we do it like amistre we would make the problem much easier but also kindof wrong
myininaya
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and kindof wrong is just wrong
donovan11
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now im confused >_<
amistre64
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horseshoe and handgranades me friend :)
myininaya
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so we have x^2-9x+20+e=0
myininaya
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oops -e
donovan11
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wouldnt it be -e?
myininaya
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Yes i blame amistre
myininaya
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lol
beens
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bring over 1 to the left at the start...before changinglg form...
amistre64
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...its my liver pills...blame the liver pills :)
donovan11
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so whats the answer?
myininaya
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use quadractic formula x=(9@sqrt(81-4(1)(20-e))/2 where @ means + or -, but make sure your answer is positive because you cannot do ln(negative)
beens
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sorry...doesn't make a difference what I said
beens
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Quadratic formula the way to go
donovan11
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this is what i put on the formula
-1+squareroot(1^2 -4(1)(20-e))))/2
myininaya
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no
myininaya
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a=1 n=-9 c=20-e correct?
beens
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c=-20-e
myininaya
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b=-9*
beens
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b=1
donovan11
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no b =1
myininaya
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dont listen to me
myininaya
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im doing two things at once sorry
donovan11
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my calculator wont work
myininaya
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(-1+sqrt(1-4(-20-e))/2=4.2925 and (-1-sqrt(1-4(-20-e))/2=-5.2925 but we can't use -5.2925 since it is negative and the natural log of a negative number doesnt exist
amistre64
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x can be negative if it is not the only thing controling the value of the log.
the thing is:
x-4 needs to be greater than 0 and,
x+5 needs to be greater than 0.
x >4 serves both cases.
myininaya
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correct!
myininaya
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that negative number gives you another negative number when you plug it into x-4