Difference between revisions of "2020 AMC 12B Problems/Problem 13"
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~ TheBeast5520 | ~ TheBeast5520 | ||
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+ | == Solution 5 (Guesstimation)== | ||
+ | Note: Only use this method if all else fails and you cannot find a way to simplify the logarithms. | ||
== Video Solution == | == Video Solution == |
Revision as of 10:52, 13 August 2021
Contents
[hide]Problem
Which of the following is the value of
Solution 1 (Observations)
Using the knowledge of the powers of and we know that and Therefore, Only choices and are greater than but is certainly incorrect--if we compare the squares of the original expression and then they are clearly not equal. So, the answer is
~Baolan
~Solasky (first edit on wiki!)
~chrisdiamond10
~MRENTHUSIASM (reformatted and merged the thoughts of all contributors)
Solution 2 (Properties of Logarithms: Direct)
Note that:
We use these properties of logarithms to rewrite the original expression: ~MRENTHUSIASM
Solution 3 (Properties of Logarithms: Stepwise)
. If we call , then we have
. So our answer is .
~JHawk0224
Solution 4 (Change of Base Formula)
First, From here, Finally, Answer:
Note that in this solution, even the most minor steps have been written out. In the actual test, this solution would be quite fast, and much of it could easily be done in your head.
~ TheBeast5520
Solution 5 (Guesstimation)
Note: Only use this method if all else fails and you cannot find a way to simplify the logarithms.
Video Solution
~IceMatrix
Video Solution
https://youtu.be/RdIIEhsbZKw?t=1463
~ pi_is_3.14
Video Solution (Meta-Solving Technique)
https://youtu.be/GmUWIXXf_uk?t=1298
~ pi_is_3.14
See Also
2020 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 12 |
Followed by Problem 14 |
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.