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

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Mohammad Sulaiman Stanekzai
回答： Mohammad Sulaiman Stanekzai 2017-12-24
How to solve this equation to find x? Thanks in advance

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采纳的回答

Birdman
Birdman 2017-12-21
编辑：Birdman 2017-12-21
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)

更多回答（4 个）

Torsten
Torsten 2017-12-21
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.
Star Strider
Star Strider 2017-12-21
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.
Image Analyst
Image Analyst 2017-12-21
Try the fzero() function.
Is this your homework?
Mohammad Sulaiman Stanekzai
Thanks in advance for your great and helpful answers :)

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