Question:

Solve for y without rounding?

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ln(y+2) = ln35-lny

no calculator.

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  1. ln(y+2)=ln(35/y)   LOG IDENTITY!!!

    so y+2=35/y

    You can solve for y now


  2. ln(y + 2) = ln(35) - ln(y)

    ln(y + 2) = ln(35/y)

    y + 2 = 25/y

    y^2 + 2y = 25

    y^2 + 2y - 25 = 0

    (-2 ± √(104))/2

    -1 ± √(26)

    Your exact answer then would be: y = {(-1 - √(26)), (-1 + √(26))}

  3. ln(y+2)=ln35-lny

    ln(y+2)+lny=ln35

    ln[y(y+2)]=ln35

    y/\2+2y-35=0

    (y-5)(y+7)=0

    y=5, y=-7
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