Please check if this is right:

If log x = a, and log y = b, what expression containing both a and b is equal to:

$\displaystyle log \left( \frac{10x^3}{\sqrt{y^3}} \right)

$

Using the logarithm properties, here is what I did:

$\displaystyle log \left( \frac{10x^3}{\sqrt{y^3}} \right) =

$

$\displaystyle log\ 10x^3 - log\ y^\frac {3}{2} =$

$\displaystyle log\ 10 + 10g x^3 - log\ y^\frac {3}{2} =$

$\displaystyle 1 + 3\ log\ x - \frac {3}{2}\ log\ y\ =$

$\displaystyle 1 + 3\ (a) - 1.5\ (b) =$

$\displaystyle 3a-1.5b+1$

Did I get it?