Writing an equation as a single log?

Question

Ok this equation is -2log3 1?x + 1/3log3 sqrt x


For some reason I keep getting 1/2log3x but I have a strong feeling that this is not correct at all can someone help me get on the right track please?

Answer 1

-2log3 1/x + 1/3log3 sqrt x =

-2( log3 1 -log3 x) + 1/3 ( 1/2 log3 x) =

-2( 0 - log3 x) +1/6 log3 x =

2 log3 x + 1/6 log3 x =

13/6 log3 x

Answer 2

-2log3 1/x + 1/3log3 sqrt x
= log3 (1/x)^-2 + log3 (x^1/2)^(1/3)
= log3 [1/(x^2+ x^(1/6)]