## anonymous 4 years ago Express in the form y=f(x): In(4-y)=In(x-2)+In(8-x)-x

1. anonymous

$e^{\ln(4-y)}=e ^{\ln(x-2)(8-x)-x}$ $4-y=\frac{(x-2)(8-x)}{e ^{x}}$ $y=-\frac{(x-2)(8-x)}{e ^{x}} + 4$ $y=\frac{x^2-10x+4e^x+16}{e^x}$

2. 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?

3. 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.