Let $$L(x) = \hbox{log}_a(x)$$ where we don't know the base $a$. However, we do know that $$L(2) = 0.36441 \quad\hbox{and}\quad L(3) = 0.57757.$$
Use this information to compute

$L(4) =$ .
$L(a^2) =$ .
$L(a^3) =$ .
$L(6^5) =$ .