The expression 2 log x - (3 log y + log z) is equivalent to...

.. 2log(x) - ( 3log(y) + log(z) )
= log(x^2) - ( log(y^3) + log(z) )
= log(x^2) - log( z*y^3 )
= log( x^2 /( z*y^3 ) )

We must use the properties: alogx = logx ^a , logx - logy = log(x/y) , logx + log y = log(x*y)

First use the property: alogx = logx ^a and get:

logx^2 - (logy^3 + logz) now use the property inside the parenthesis:

logx^2 - (log(y^3 * z) and the other property: log (x^2) /(y^3*z) OK!

according to logarithmic rulez...:
2 log x - (3 log y + log z) = log(x^2) - (log(y^3) + log z) = log(x^2) - log z*(y^3) = log (x^2)/(z*(y^3))