Show that for all real numbers a and b with a > 1 and b> 1, if f(x) is O(logbx), then f(x) is O(logax).

Step 1:

In this problem, we have to show that if f(x) is O(logbx), then f(x) is O(logax) for all real numbers a and b with a > 1 and b> 1.

Step 2:

As we know about Big-O notation: if f and g are real-valued functions such that f(x) is O(g(x)).We can say that f(x) is O(g(x)) if there are constant C and k such that |f(x)||g(x)| whenever x>k

Now, we can write logbx =Similarly for logax =