1950 AHSME Problems/Problem 37
Problem
If $y \equal{} \log_{a}{x}$ (Error compiling LaTeX. ! Undefined control sequence.), , 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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