$\scriptsize \log_{24}(48)+\log_{12} (54)>4$ (Continued)

Have you tried out any other approaches that you could think of to solve the previous "$ \log_{24}(48)+\log_{12} (54)>4$"?

At any rate, that is one very tough problem and it could cause you lose sleep over it if you're persistent enough and have the absolute determination to prove the statement. But, we know as it have been our experience that nothing would be more frustrating and aggravating that when we put up the titanic fight to solve for the problem, the attempts at the solution were never correct. After the complete failures, you began to wonder if the extra effort would hardly be worth it and if you should just ditch the problem in the first place once you realized there is nothing that you could have thought to tackle the problem successfully. 

Yes, this seems like it would be a task of immense intelligence effort to prove for this logarithmic inequality where $\left(\log_{24}(48) \right)^2+ \left(\log_{12}(54) \right)^2 >4$.

We will lead you to the solution at this post and read on, as the solution will open your eyes: