What's the name for a distribution of the form $10^D$, where $D$ is a known distribution? In my particular case, I'm generating uniformly random numbers and using them as the power to a base-10 exponent, e.g. in R:
s <- 10^runif(10, 1, 10)

Is there a name for this distribution, i.e., $s \sim 10^{\mathcal{U}(1,10)}$?
Sorry if this is poorly worded, if you understand what I'm asking you can feel free to edit this post to clarify it. 
 A: Note that $10^D = \exp(kD)$  (where $k=\ln(10)$); your uniform on (1,10) is still uniform when you multiply it by $k$, so (by analogy with distributions like the log-normal, whose log is normal and the log-logistic, whose log is logistic), we might call it log-uniform.
And indeed, when $D$ is normal, $10^D$ is log-normal, so this fits quite well.
[However, that usage isn't always consistent across distributions.]
A: I do not think it has a name, but it loosely resembles Exponential distribution with $\lambda = 1$ and uniformly distributed $x$'s. Notice however that you get something strange of it, since as Uniform distribution is
$$
f(x) = \begin{cases}
\frac{1}{b - a} & \mathrm{for}\ a \le x \le b, \\
0 & \mathrm{for}\ x<a\ \mathrm{or}\ x>b
\end{cases} 
$$
then if $U \sim \mathcal{U}(a, b)$ and $s = 10^U$, you get
$$
f(x) = \begin{cases}
10^{\frac{1}{b - a}} & \mathrm{for}\ a \le x \le b, \\
1 & \mathrm{for}\ x<a\ \mathrm{or}\ x>b
\end{cases} 
$$
and I am not sure if this is what you were thinking of...
