solve the following exponential equation.
(e^x-e^-x)/2=6
what is the exact answer?
x=?
what is the answer approx to 3 decimal places?
x=?
(e^x-e^-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
(y-4)(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