1950 AHSME Problems/Problem 37
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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