proof verification - Proving a log by induction

I had a test recently and there was a log question that was

$$3\log_3(x) - 4\log_3(x) + 1/2\log_3(x).$$ When I solved it I got $$\log_3 \left(\frac{1}{\sqrt{x}}\right).$$ My teacher says that is incorrect, so I asked many people and they said I was correct. She said the only way I could get points back was if I prove it by induction, which I do not know what that is. I was wondering if my answer was right and if so how would I prove it by induction if thats possible? Thanks for all your help. Its critical I get these points back