anonymous
  • anonymous
Express in the form y=f(x): In(4-y)=In(x-2)+In(8-x)-x
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
\[e^{\ln(4-y)}=e ^{\ln(x-2)(8-x)-x}\] \[4-y=\frac{(x-2)(8-x)}{e ^{x}} \] \[y=-\frac{(x-2)(8-x)}{e ^{x}} + 4\] \[y=\frac{x^2-10x+4e^x+16}{e^x}\]
anonymous
  • anonymous
thax loads anhhuyalex,i understand the first three steps but not the last one-may you please elaborate how we got 4e^x or which rule are we using?
anonymous
  • anonymous
the last step is \[y=-\frac{-x^2+10x-16}{e^x}+4=\frac{x^2-10x+16}{e^x}+4=\frac{x^2-10x+16+4e^x}{e^x}\] because 4e^x/e^x is essentially 4. I'm only using algebra to manipulate the last bit.

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