Can anybody explain in detail step by step how dowe get from `y=(x^2-5x+4)/e^x+2` ,to `y=(x^2-5x+4+2e^x)/e^x`  ?Is this an answer of `ln(2-y)=ln(x-1)+ln(4-x)-x?`

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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`ln(2-y) = ln (x-1) + ln(4-x) - x`

Fist we will re-wrie x as natural logarith to simplify using logarithm properties. ==> `x = ln e^x`

`` `ln (2-y) = ln(x-1) + ln(4-x) - ln e^x`

Now we will use logarith properties to simplify :

`ln a + ln b = ln (ab)`

`ln a - ln b = ln (a/b) `

`==gt ln a + ln b - ln c = ln ((ab)/c)`

`ln(2-y)= ln(((x-1)(4-x))/e^x)`

`==> ln(2-y)= ln ((-x^2 +5x -4)/e^x)`

`==> 2-y = (-x^2+5x-4)/e^x`

`==> -y = (-x^2+5x-4)/e^x -2`

`==> -y = (-x^2+5x-4 -2e^x)/e^x`

`==> y= -(-x^2+5x-4-2e^x)/e^x`

`==> y= (x^2-5x+4+2e^x)/e^x`

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