Before calculators were widely available people used logarithm tables to simplify multiplication and division, using the fact that the logarithm of a product equals the sum of the logarithms and the logarithm of the quotient equals the difference of the logarithms.
These tables were constructed by computing laboriously and carefully the logarithms of a few selected numbers and then combining the logarithms using the rules just mentioned.
This exercise suggest how the process may have worked.
Let $$L(x) = \hbox{log}_a(x)$$ where we don't know the base $a$. However, we do know that $$L(2) = 0.39051 \quad\hbox{and}\quad L(3) = 0.61895.$$
Use this information to compute

$L(6)=$ .
$L(9) =$ .
$L(12) =$ .
$L\left(\frac{2}{3}\right) =$ .
$L\left(3^{10}\right) =$ .
$L(1) =$ .