Logarithmic-analytic functions are iterated compositions (from either side) of globally subanalytic functions (i.e. functions definable in the o-minimal structure $\R_{an}$ of restricted analytic functions) and the global logarithm. Their definition is kind of hybrid. From the viewpoint of logic, log-analytic functions are definable in the o-minimal expansion $\R_{an,exp}$ of $\R_{an}$ by the global exponential function; in fact they generate the whole structure $\R_{an,exp}$. But from the point of analysis their definition avoids the exponential function and should therefore also not exhibit properties of the function $\exp(−1/x)$ as flatness or infinite differentiability but not real analyticity. This seems to be obvious. But the problem is that a composition of globally subanaytic functions and the logarithm allows a representation by ’nice’ terms only piecewise. Moreover, the ’pieces’ are in general not definable in $\R_{an}$ but only in $\R_{an,exp}$. And the existing preparation results for log-analytic functions involve functions which are not log-analytic. But by elaborating on the preparation theorems one can identify situations where the preparation can be carried out inside the log-analytic category. And these situations are sufficient to obtain the following results: We show that the derivative of a log-analytic function is log-analytic. We prove that log-analytic functions exhibit strong quasianalytic properties. We establish the parametric version of Tamm’s theorem for log-analytic functions. It seems also to be obvious that log-analytic functions are polynomially bounded. This is indeed true in the univariate case. But, surprisingly, multivariate log-analytic functions can exhibit exponential growth. We give examples and present structural results on the growth.