Difference between revisions of "1950 AHSME Problems/Problem 37"
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==Problem== | ==Problem== | ||
− | If <math> y | + | If <math> y = \log_{a}{x}</math>, <math> a > 1</math>, which of the following statements is incorrect? |
<math>\textbf{(A)}\ \text{If }x=1,y=0 \qquad\\ | <math>\textbf{(A)}\ \text{If }x=1,y=0 \qquad\\ |
Revision as of 23:13, 4 April 2015
Problem
If , , which of the following statements is incorrect?
Solution
Let us first check
. Rewriting into exponential form gives . This is certainly correct.
. Rewriting gives . This is also certainly correct.
. Rewriting gives . Because , therefore positive, there is no real solution to , but there is imaginary.
. Rewriting: such that . Well, a power of can be less than only if . And we observe, has no lower asymptote, because it is perfectly possible to have be ; in fact, the lower gets, approaches . This is also correct.
. This is the last option, so it follows that our answer is
See Also
1950 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 36 |
Followed by Problem 38 | |
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All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.