integration – Let $f(x)$ determine the value of $g(x)$ in terms of $f(x)$


Let $f(x)$ determine the value of $g(x)$ in terms of $f(x),$ my teacher tells me that the solution is between sustitution, i attemped $u = log(x) ,du = frac{1}{x},dx$, $dx = e^u,du$, also my teacher says that the interval of integration won’t be the same but it’s possible to split the integral, sorry im not native english speaker lol

$$f(x) = int_0^x e^{e^t} , dt$$
$$g(x) =int_2^3 frac{dx}{log(x)}$$