  It is well known that value at a non-zero algebraic number of each of the
functions $e^{x}, \ln x, \sin x, \cos x, \tan x, \csc x, \sec x, \cot x, \sinh
x,$ $ \cosh x,$ $ \tanh x,$ and $\coth x$ is transcendental number (see Theorem
9.11 of \cite{N}). In the work, we show that for any one of the above mentioned
functions, $f(x)$, and for a polynomial $g(x)$ with rational coefficients the
zero, if any, of the equation $f(x)=g(x)$ is a transcendental number. We also
show that if $f(x)$ and $g(x)$ are polynomials with rational coefficients, then
a zero of the equation $e^{f(x)}=g(x)$ is a transcendental number. Finally we
show that the existence of an abelian group whose non-zero elements are
transcendental numbers.
