solve analytically ex15ex8SolutionMove everything to one sid

solve analytically

e^x+15e^-x=8

Solution

Move everything to one side:
e^x +15e^-x - 8= 0
put e^x=y
y + 15/y - 8 = 0
Multiply everything by y to cancel off the denominator:
y^2 -8y +15 = 0
Factor it out:
(y - 5)(y - 3) = 0
Solve for each:
y - 5 = 0
y = 5
y-3=0

y=3

Now substitute e^x back for y and solve for each:

e^x = 5
x = ln5

and e^x=3

x=ln3

hence x=ln5,ln3