Answer
The series converges for all values of $x$. The interval of convergence is $R$ and radius of convergence is $\infty$.
Work Step by Step
$10^{x}=\Sigma_{n=0}^\infty(x)^{n}\frac{(ln10)^{n}}{n!}$
$\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\frac{\frac{(ln10)^{n+1}x^{n+1}}{n+1!}}{\frac{(ln10)^{n}x^{n}}{n!}}|$
$\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\frac{xln10}{n+1}|$
$=0$
$=0 \lt 1$
Thus, the series converges for all values of $x$. The interval of convergence is $R$ and the radius of convergence is $\infty$.
