Difference between revisions of "1958 AHSME Problems/Problem 12"
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==Problem== | ==Problem== | ||
| − | If <math> P | + | If <math> P = \frac{s}{(1 + k)^n}</math> then <math> n</math> equals: |
| − | <math> \textbf{(A)}\ \frac{\log{\left(\frac{s}{P}\right)}}{\log{(1 | + | <math> \textbf{(A)}\ \frac{\log{\left(\frac{s}{P}\right)}}{\log{(1 + k)}}\qquad |
| − | \textbf{(B)}\ \log{\left(\frac{s}{P(1 | + | \textbf{(B)}\ \log{\left(\frac{s}{P(1 + k)}\right)}\qquad |
| − | \textbf{(C)}\ \log{\left(\frac{s | + | \textbf{(C)}\ \log{\left(\frac{s - P}{1 + k}\right)}\qquad \\ |
| − | \textbf{(D)}\ \log{\left(\frac{s}{P}\right)} | + | \textbf{(D)}\ \log{\left(\frac{s}{P}\right)} + \log{(1 + k)}\qquad |
| − | \textbf{(E)}\ \frac{\log{(s)}}{\log{(P(1 | + | \textbf{(E)}\ \frac{\log{(s)}}{\log{(P(1 + k))}}</math> |
==Solution== | ==Solution== | ||
| Line 24: | Line 24: | ||
==See also== | ==See also== | ||
| − | {{AHSME box|year=1958|num-b=11|num-a=13}} | + | {{AHSME 50p box|year=1958|num-b=11|num-a=13}} |
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 22:08, 13 March 2015
Problem
If 
then 
equals:
Solution
![\[P=\frac{s}{(1+k)^n}\]](http://latex.artofproblemsolving.com/a/a/9/aa949293e2c9d673b8207d0ffafed7a26c165edd.png)
![\[(1+k)^n=\frac{s}{P}\]](http://latex.artofproblemsolving.com/8/6/5/865792d594fcb28f9fa40a0f0a6f81a1a2ecab78.png)
Take the 
of each side.
![\[n \log(1+k) = \log\left(\frac{s}{P}\right)\]](http://latex.artofproblemsolving.com/9/d/8/9d82f2f5be7a5b25b973e0064949358bdfc653b3.png)
![\[n = \frac{\log\left(\frac{s}{P}\right)}{\log(1+k)} \to \boxed{\text{(A)}}\]](http://latex.artofproblemsolving.com/e/3/9/e39a69e3b1cc48a024e6349ad46f82ba8d1479ab.png)
See also
| 1958 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 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 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
