Difference between revisions of "2006 Alabama ARML TST Problems/Problem 5"
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==Problem== | ==Problem== | ||
− | There exist positive integers <math>A</math>, <math>B</math>, <math>C</math>, and <math>D</math> with no common factor greater than 1, such that | + | There exist positive integers <math>A</math>, <math>B</math>, <math>C</math>, and <math>D</math> with no [[greatest common divisor|common factor]] greater than 1, such that |
<center><math>A\log_{1200} 2+B\log_{1200} 3+C\log_{1200} 5=D.</math></center> | <center><math>A\log_{1200} 2+B\log_{1200} 3+C\log_{1200} 5=D.</math></center> | ||
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==See also== | ==See also== | ||
{{ARML box|year=2006|state=Alabama|num-b=4|num-a=6}} | {{ARML box|year=2006|state=Alabama|num-b=4|num-a=6}} | ||
− | + | [[1995 AHSME Problems/Problem 24|A similar problem]] | |
− | [[1995 AHSME Problems/Problem 24]] | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] |
Latest revision as of 09:12, 1 April 2009
Problem
There exist positive integers , , , and with no common factor greater than 1, such that
Find .
Solution
Simplifying and taking the logarithms away,
Therefore, , , and . Since and are relatively prime, , , , .
See also
2006 Alabama ARML TST (Problems) | ||
Preceded by: Problem 4 |
Followed by: Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |