2006 Cyprus MO/Lyceum/Problem 10

Revision as of 10:37, 27 April 2008 by I like pie (talk | contribs) (Standardized answer choices)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

If $2^x=15$ and $15^y=256$, then the product $xy$ equals

$\mathrm{(A)}\ 7\qquad\mathrm{(B)}\ 3\qquad\mathrm{(C)}\ 1\qquad\mathrm{(D)}\ 8\qquad\mathrm{(E)}\ 6$

Solution

$(2^x)^y = 2^{xy} = 256$, so $xy = 8\ \mathrm{(D)}$.

See also

2006 Cyprus MO, Lyceum (Problems)
Preceded by
Problem 9
Followed by
Problem 11
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 26 27 28 29 30
Invalid username
Login to AoPS