3= 2*(e^x - e^-x)

How to solve this equation to find x? Thanks in advance

Answer 1

[Birdman]

syms x
eq=3==2*(exp(x)-exp(-x));
sol=vpasolve(eq)

If you solve it with solve command, you will obtain two roots, but one of them is a complex solution. Therefore, I directly solved it with vpasolve. But also see the solution for the solve command. The result is 0.6932.

sol=solve(eq)

[Mohammad Sulaiman Stanekzai]

Thank you Sir :) it worked perfectly.

Answer 2

[Torsten]

Substitute

e^x = y.

This leads to

y - 1/y = 3/2

or

y^2 - 3/2*y - 1 = 0.

Thus

y = 3/4 + sqrt(25/16) = 2.

Then

x = log(y) = log(2).

Or use

xsol = solve(3==2*(exp(x)-exp(-x)),x)

Best wishes

Torsten.

Answer 3

[Star Strider]

Much simpler, because your equation is equivalent to 4*sinh(x):

xarg = @(y) asinh(y/4)
Result = xarg(3)

Result =
   0.693147180559945

Even the anonymous function is not necessary. I added it to convenience.

Answer 4

[Image Analyst]

Try the fzero() function.

Is this your homework?

Answer 5

[Mohammad Sulaiman Stanekzai]

Thanks in advance for your great and helpful answers :)