Difference between revisions of "1983 AIME Problems/Problem 1"
Luimichael (talk | contribs) (→Solution) |
Luimichael (talk | contribs) (→Alternative Solution) |
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Hence, <math> \log_z w = 60</math>. | Hence, <math> \log_z w = 60</math>. | ||
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+ | --[[User:Luimichael|Luimichael]] 22:46, 19 November 2007 (EST) | ||
== See also == | == See also == |
Revision as of 22:46, 19 November 2007
Contents
[hide]Problem
Let ,, and all exceed , and let be a positive number such that , , and . Find .
Solution
The logarithmic notation doesn't tell us much, so we'll first convert everything to the equivalent exponential expressions.
, , and . If we now convert everything to a power of , it will be easy to isolate and .
, , and .
With some substitution, we get and .
Alternative Solution
Applying Change of Base Formula:
Therefore, .
Hence, .
--Luimichael 22:46, 19 November 2007 (EST)
See also
1983 AIME (Problems • Answer Key • Resources) | ||
Preceded by First Question |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |