1950 AHSME Problems/Problem 42
Problem
The equation is satisfied when is equal to:
Solution
Solution 1:
Taking the log, we get , and . Solving for x, we get , and
Solution 2:
is the original equation. If we let , then the equation can be written as . This also means that , considering that adding one to the start and then taking that to the power of does not have an effect on the equation, since is infinitely long in terms of raised to itself forever. It is already known that from what we first started with, so this shows that . If , then that means that .
This is just a faster way once you get used to it, instead of taking a log of the function.
~mathmagical
See Also
1950 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 41 |
Followed by Problem 43 | |
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