MATLAB: The answer is like that

resultsolve

syms x
s = vpa(solve((0.5)==(log(5)*log10(8)*sinh(x))/(atan(0.5)*(3^(1/5))*abs(cos(2*pi/3))*exp(cos(2*pi/3))),x))
the correct result of this equation is 0,06 but when i run this command matlab gives me this
s =
0.060219526083180976165227748603359
- 0.060219526083180976165227748603359 + 3.1415926535897932384626433832795i
So, why i found this result and how can i found just " 0,06 " ?
Thank you

Best Answer

0.06 is not a solution to that equation. If you substitute 0.06 for x you get
0.5 == 0.49817509413836472619769716883263
which is false.
The exact solution is asinh((3^(1/5)*atan(1/2)*exp(-1/2)*log(10))/(4*log(5)*log(8)))