Big-O Notation regarding logarithms

Question

I got asked an interview question that wanted me to discern the Big-O notation of several logarithmic functions. The functions were as follows:

f(x) = log⁵

Answer 1

f(x) = log^5(n)
f(x) = log(n^5) -> 5 log(n)
O(5 log(n)) < O(log(n)^5)

f(x) = log(6*log n) -> log(6)+log(log(n))
f(x) = log(log n) 
log(log n) < log(6) + log(log(n)) 

, although log(6) is a constant so they have same O