solve for x ex 16ex2 4Solutionex 16ex2 4 ex 16ex 42 ex

solve for x: e^x + 16e^-x/2 = 4

(e^x + 16*e^-x)/2 = 4

(e^x + 16*e^-x) = 4*2

(e^x + 16/e^x) = 8

(e^2x + 16)/e^x = 8

e^2x + 16 = 8*e^x

Put e^x = t

t^2 + 16 = 8*t

t^2 - 8*t + 16 = 0

(t - 4)^2 = 0

Which gives us

t = 4

this means

e^x = 4

ln (e^x) = ln 4

x = ln 4 = 2*0.693

x = 1.386