Melody

I'll just do the first one for you.

$$\\g(x) = log_3( x^2-9)\\\\
x^2-9>0\qquad \qquad \mbox{because you can only find the log of a positive number}\\\\
x^2>9\\\\
x<-3 \:\:or\:\: x>3$$

Check with a graph.

I am just going to do the first one for you.    (Completed after Alan's comment below)

1)   e ^x = 3

$$\\log_e3=x\\\\
x=ln3$$

Dpo the others the same way.

That is true Alan but what I was experimenting with is how this web2.0calc would interpret 

10000e-2.835

So I plugged it in and this is what I got.  So the web2 calc does not interpret it this way.

$$\mathrm{ERROR}$$

Your question needs brackets to make it unambiguous.

Is this is what you have asked.

$$15x^{1/2}y^{1/12}/(24x^{5/6}y^{1/6})\\\\
=\frac{15}{24}x^{1/2-5/6}y^{1/12-1/6}\\\\
=\frac{5}{8}x^{3/6-5/6}y^{1/12-2/12}\\\\
=\frac{5}{8}x^{-2/6}y^{-1/12}\\\\
=\frac{5}{8y^{1/3}y^{1/12}}$$

Thanks Chris, I will have  to have a play. 

sevenUP already answered this question here

I just google it Roasala and I found out that rm is Malaysian Ringgit    (I just googled "rm money")

I always do these as ratio questions.  I find them easier that way.

$$\frac{1500}{12.5grams}=\frac{x}{1g}\\$$

g=1500/12.5 = 120

1g costs rm120

Twenty-five to the power of minus two x squared x minus two equals five hit in five

Thank you Rosala but the bits in red still do not make much sense.  

$$x^2x^2x^2x^2x^2x^2x^2\\
=x^{2+2+2+2+2+2+2}\\
=x^{14}$$