coshx = 5/3 ; solve for x

Question

 solve the following equations for x

 

a. tanhx = 12/13

 

b. sinhx = 3/4

 

c. coshx =5/3

Answer 1

If sinh x = 3/4, then  (e^x -e^-x) = 1.5 and you can solve this empirically on a graphing calculator.

or Let e^x = t and rewrite this equation as t + 1/t = 1.5;

t² + 1 = 1.5t

t² -1.5t + 1 = 0; solve for t using quadratic formula, then solve for x.