Difference between revisions of "1993 AHSME Problems/Problem 11"
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== Problem == | == Problem == | ||
− | If <math>log_2(log_2(log_2(x)))=2</math>, then how many digits are in the base-ten representation for x? | + | If <math>\log_2(\log_2(\log_2(x)))=2</math>, then how many digits are in the base-ten representation for x? |
<math>\text{(A) } 5\quad | <math>\text{(A) } 5\quad |
Latest revision as of 22:11, 27 May 2021
Problem
If , then how many digits are in the base-ten representation for x?
Solution
Taking successive exponentials and
and
. Now
and
so we can approximate
which has 5 digits. In general,
has approximately
digits.
See also
1993 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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 |
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