Difference between revisions of "2018 AMC 10A Problems/Problem 14"
(→Solution) |
(→Solution) |
||
Line 20: | Line 20: | ||
<cmath>2^{100} \leq 2^{96}*3^4.</cmath> | <cmath>2^{100} \leq 2^{96}*3^4.</cmath> | ||
This means that our original value, <math>x</math>, must be less than <math>81</math>. The only answer that is less than <math>81</math> is <math>80</math> so our answer is <math>\boxed{A}</math>. | This means that our original value, <math>x</math>, must be less than <math>81</math>. The only answer that is less than <math>81</math> is <math>80</math> so our answer is <math>\boxed{A}</math>. | ||
+ | |||
+ | ~Nivek |
Revision as of 14:44, 8 February 2018
What is the greatest integer less than or equal to
Solution
Let's set this value equal to . We can write
Multiplying by
on both sides, we get
Now let's take a look at the answer choices. We notice that
, choice
, can be written as 3^4. Plugging this into out equation above, we get
The right side is larger than the left side because
This means that our original value,
, must be less than
. The only answer that is less than
is
so our answer is
.
~Nivek