Question

(e^x-e ^(-x))/(2)=3 solve for x and answer should have 3 decimal places

Answer 1

(e^x-e^-x)/2=3,

e^x-e^-x=6,

e^2x-1=6e^x,

e^2x-6e^x-1=0 is a quadratic equation.

e^2x-6e^x=1,

e^2x-6e^x+9=10,

(e^x-3)²=10,

e^x-3=±√10,

e^x=3±√10. e^x cannot be negative so e^x=3+√10 and x=ln(3+√10)=1.8184 approx.

(e^x-e^-x)/2=3 is the same as sinh(x)=3. x=sinh^-1(3) gives the same answer.