2020 AMC 12B Problems/Problem 13
Contents
Problem
Which of the following is the value of
Solutions
Solution 1 (Logic)
Using the knowledge of the powers of and
, we know that
is greater than
and
is greater than
Only choices
and
are greater than
but
is certainly incorrect--if we compare the squares of the original expression and E, they are clearly not equal. So, the answer is $\boxed{\textbf{(D) } \sqrt{\log_2{3}}+\sqrt{\log_3{2}}.$ (Error compiling LaTeX. Unknown error_msg)
Written collectively:
~Baolan
~Solasky (first edit on wiki!)
~chrisdiamond10
~MRENTHUSIASM
Solution 2
. If we call
, then we have
. So our answer is
.
~JHawk0224
Solution 3
From here,
Finally,
Answer:
~ TheBeast5520
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.
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.