Arrange the following set in ascending order:
{(n log n^2), 2^n, log 20, 120, log 10, (n^2 log n^2) }
I believe it is :
{log20, log10, (n log n^2), (n^2 log n^2), 2^n, 120}
Couple of points:
1. Comparing the expressions with 'n' in them to the ones that don't - it really depends what the value of 'n' is. For example if n=1 then log(n) = 0 and so n log(n^2) = 0, which is less than log 10 or log 20. But if n = 10 then 10 log 10^2 = 10 log (100), which is greater than log(10) or log(20).
2. Remember that the log function is monotonically increasing, so log(20) > log(10).