Sinh (2Lnx)

Solve for x over the real numbers:
sinh(2 log(x)) = 0

Take the inverse hyperbolic sine of both sides:
2 log(x) = 0

Divide both sides by 2:
log(x) = 0

Cancel logarithms by taking exp of both sides:
Answer: |x = 1

sinh(2ln x)

= \(\dfrac{1}{2}(e^{2\ln x}-e^{-2\ln x})\)\(\text{<----By definition}\)

=\(\dfrac{(e^{\ln x})^{2}}{2}-\dfrac{1}{2(e^{\ln x})^{2}}\)

=\(\dfrac{x^2}{2}-\dfrac{1}{2x^2}\)