Basic understanding of Log and $2 \log _3(x)+\log _9(x)=10$ So this is what I have done so fare 
$$2 \log _3(x)+\log _9(x)=10$$
I know that 
$$\log _9(x)=\log _3\left(\sqrt{x}\right)$$
I therefore have
$$\log _3\left(x^{5/2}\right)=10$$
However here is where I realise that I have not properly understood the underlying of log.
Since I know that the answer is 81 I was able to realise that 
$$\log _3(x)=4$$
Is the same as x==3^4, but  I do not understand if Im dividing or multiplying or what is going on. I thought that 
$$\log _3(x)$$
meant that
$$3^?=x$$
Basically trying to find the exponent? At least that is the dummed version that I got thought in class
Could someone explain what is going on and what I do not understand , in such a way that I am able to grasp the concept.

You correctly got:$$\log_3(x^{5/2})=10$$next step gives you:$$x^{5/2}=3^{10}$$therefore:$$x=(3^{10})^{2/5}$$Hopefully you can complete from here
