this is part of a larger question for hyperbolic functions, but i feel if i get this the rest will come into place...what is x of tanh x= 3/4, or you can solve the below equation
3/4=(e^x - e^-x)/(e^x + e^-x)
any help is very appreciated
this is part of a larger question for hyperbolic functions, but i feel if i get this the rest will come into place...what is x of tanh x= 3/4, or you can solve the below equation
3/4=(e^x - e^-x)/(e^x + e^-x)
any help is very appreciated
Yeah there is. You can use standard algebraic techniques and logs. Ignore the second solution if you only want a real answer
$\displaystyle 3e^x+3e^{-x} = 4e^x-4e^{-x}$
$\displaystyle e^x-7e^{-x} = 0
$
$\displaystyle e^x - \frac{7}{e^x} = 0$
$\displaystyle e^{2x} - 7 = 0$
$\displaystyle (e^x-\sqrt{7})(e^x+\sqrt{7}) = 0$
$\displaystyle x = \frac{1}{2}ln(7)$ or $\displaystyle x = \frac{1}{2}ln(-7) = \frac{1}{2}ln(7)+ i \left(\frac{\pi}{2}\right)$