4. [10] An algorithm whose runtime grows according to n log10 n takes 1 second to run on an input with n= 1000. In trying to estimate the runtime when n = 10000, we observe that the new n is 10x the old n and conclude that the new runtime should be a factor of 102 log10 10 greater; i.e., the new runtime should be 100x the old runtime or 100 seconds. Is this analysis correct? If yes, argue that this analysis is correct. If no, explain why it's incorrect and what the correct analysis is