For problems 10 and 11 solve the exponential equation for th

For problems 10 and 11, solve the exponential equation for the variable. When necessary, round to three decimal places. e^2x - 6e^x - 55 = 0

e^2x - 6e^x - 55 =0

Plug y = e^x

So, y^2 - 6y - 55 =0

Its qaudratic equation solve by factorisation :

y^2 - 11y + 5y - 55 =0

y( y -11) + 5(y -11) =0

(y + 5)( y -11) =0

y = -5 ; y = 11

Now neglect y = -5 = e^x as exponetial function can never be -ve

So, e^x = 11 ; x = ln(11) = 2.397

x = 2.398