Difference between revisions of "2002 AMC 12P Problems/Problem 24"
(Created page with "== Problem == How many positive integers <math>b</math> have the property that <math>\log_{b} 729</math> is a positive integer? <math> \mathrm{(A) \ 0 } \qquad \mathrm{(B...") |
(→See also) |
||
Line 8: | Line 8: | ||
== See also == | == See also == | ||
− | {{AMC12 box|year= | + | {{AMC12 box|year=2002|ab=P|num-b=23|num-a=25}} |
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 00:26, 30 December 2023
Problem
How many positive integers have the property that
is a positive integer?
Solution
If , then
. Since
,
must be
to some factor of 6. Thus, there are four (3, 9, 27, 729) possible values of
.
See also
2002 AMC 12P (Problems • Answer Key • Resources) | |
Preceded by Problem 23 |
Followed by Problem 25 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.