Difference between revisions of "1993 AHSME Problems/Problem 10"
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== Solution == | == Solution == | ||
| − | We have | + | We have <math>r=(3a)^{3b}</math> |
| − | <math>r=(3a)^{3b}</math> | + | |
| − | + | From this we have the equation <math>(3a)^{3b}=a^bx^b</math> | |
| − | From this we have the equation | + | |
| − | <math>(3a)^{3b}=a^bx^b</math> | + | Raising both sides to the <math>\frac{1}{b}</math> power we get that <math>27a^3=ax</math> or <math>x=27a^2</math> |
| − | Raising both sides to the <math>\frac{1}{b}</math> power we get that | + | |
| − | <math>27a^3=ax</math> | ||
| − | <math>x=27a^2</math> | ||
<math>\fbox{C}</math> | <math>\fbox{C}</math> | ||
Latest revision as of 21:00, 27 May 2021
Problem
Let 
be the number that results when both the base and the exponent of 
are tripled, where 
. If equals the product of and 
where 
, then 
Solution
We have 
From this we have the equation 
Raising both sides to the 
power we get that 
or 
See also
| 1993 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 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. 
