We have to use the following log rules here
[tex] a log (b) = log b^a , log(a) + log(b) = log(ab), log (a)-log(b) = log(a/b) [/tex]
So for the given question , that is
[tex] 18log \sqrt x +9 log \sqrt [3]{x}-log 10 = log(x^{18/2}) + log(x^{9/3})-log 10 [/tex]
[tex] log(x^9)+log(x^3)-log 10= log(x^9*x^3)-log 10 [/tex]
[tex] =log(x^{12}) - log 10 = log(\frac{x^{12}}{10}) [/tex]
