Difference between revisions of "1967 AHSME Problems/Problem 26"
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== Solution == | == Solution == | ||
| − | <math>\fbox{C}</math> | + | Since 1024 is greater than 1000. |
| + | |||
| + | log 1024 > 3 | ||
| + | |||
| + | 10 * log 2 > 3 | ||
| + | |||
| + | and log 2 > 3/10. | ||
| + | |||
| + | |||
| + | Similarly, 8192 < 10000, so log 8192 < 4 | ||
| + | |||
| + | 13 * log 2 < 4 | ||
| + | |||
| + | and log 2 < 4/13 | ||
| + | |||
| + | |||
| + | Therefore 3/10 < log 2 < 4/13 | ||
| + | so the answer is <math>\fbox{C}</math> | ||
== See also == | == See also == | ||
Revision as of 21:56, 9 July 2015
Problem
If one uses only the tabular information 
, 
, 
, 
, 
, 
, then the strongest statement one can make for 
is that it lies between:
Solution
Since 1024 is greater than 1000.
log 1024 > 3
10 * log 2 > 3
and log 2 > 3/10.
Similarly, 8192 < 10000, so log 8192 < 4
13 * log 2 < 4
and log 2 < 4/13
Therefore 3/10 < log 2 < 4/13
so the answer is 
See also
| 1967 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 25 |
Followed by Problem 27 | |
| 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 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
