college alg
posted by MYA on .
solve the following exponential equation.
(e^xe^x)/2=6
what is the exact answer?
x=?
what is the answer approx to 3 decimal places?
x=?

(e^xe^x)/2=6
e^x  e^x = 12
multiply each term by e^x
(e^x)^2  1 = 12e^x
let y = e^x
y^2 1 = 12y
y^2  12y  1 = 0
(y4)(y+3) = 0
y = 4 or y = 3
e^x = 4 or e^x = 3 , the latter part being impossible
so e^x = 4
take ln of both sides
ln e^x = ln4
x lne = ln4
x = ln4 or appr 1.386