Logarithims!

23)

  $$log_3(2x)^2\\ =2log_3(2x)\\ =2(log_3(2)+log_3(x)) \\ =2log_3(2)+2log_3(x) \\$$

30)

$$log_29=\frac{log9}{log2}$$     And you can finish it with a calculator.

44)

$$\frac{1}{2}log_215-log_5\sqrt{75}\\\\ =\frac{1}{2}log_2(5*3)-log_5(25*3)^{1/2}\\\\ =log_2(5*3)^{1/2}-log_5(25*3)^{1/2}\\\\ =log_2(5^{1/2}*3^{1/2})-log_5(25^{1/2}*3^{1/2})\\\\ =log_2(5^{1/2}*3^{1/2})-[log_5(5*3^{1/2})]\\\\ =log_2\;5^{1/2}+log_2\;3^{1/2}-[log_5\;5+log_53^{1/2}]\\\\ =log_2\;5^{1/2}+log_2\;3^{1/2}-[1+log_53^{1/2}]\\\\ =log_2\;5^{1/2}+log_2\;3^{1/2}-\frac{2}{2}-\frac{1}{2}log_53\\\\ =\frac{1}{2} [log_2\;5+log_2\;3-2-log_53]\\\\$$

I was working this out as I was writing the code so it is probably not the best way.

Plus i am not very happy with the answer, but this is as far as I get. 

Maybe someone esle will do something more/different.  (Are you sure the base (little) numbers were correct?)

Look at this question again. You are trying to simplify this. Maybe try simplifying by breaking 75 into 2 different numbers (15/5)

Meoldy this for you for #44