Exercise 3: A Tripling Loop — Possible Solution
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GIVEN
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i starts at 1, and i *= 3 each iteration, continuing until i >= n.
n = 1,000,000.

STEP 1: THE BIG-O CLASS
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Per this chapter's own Gotcha 2, a loop variable that grows
MULTIPLICATIVELY (here, tripling each iteration) rather than by a
fixed increment gives O(log n), not O(n) - the same reasoning as the
chapter's own doubling-loop example, just with a different base.

STEP 2: COMPUTING THE EXACT ITERATION COUNT
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Tracking i after each iteration (starting at i=1):

  Iteration 1:  i = 3
  Iteration 2:  i = 9
  Iteration 3:  i = 27
  ...continuing to triple each time...
  Iteration 13: i = 3^13 = 1,594,323 (first value >= 1,000,000)

Checking iteration 12: i = 3^12 = 531,441, which is still less than
1,000,000, so the loop has not yet stopped.

So the loop runs exactly 13 times before i first reaches or exceeds
1,000,000.

STEP 3: CONFIRMING AGAINST log BASE 3
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log base 3 of 1,000,000 ~= 12.58, and the loop must run a whole
number of times, rounding up to the next complete iteration: 13 -
matching the direct count exactly, per this chapter's own O(log n)
classification (using base 3 instead of base 2, though the Big-O
class itself, O(log n), doesn't depend on which base is used).

WHY THIS WORKS AS AN ANSWER
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The Big-O classification is justified using this chapter's own
Gotcha 2 reasoning about multiplicative loop variables, and the exact
iteration count is both traced step by step and independently
confirmed against the log-base-3 calculation, matching the same two-
method verification approach this chapter's own doubling-loop example
used.