1983 AIME Problems/Problem 1
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 exponents.
,
, and
. If we now convert everything to a power of
, it will be easy to isolate
and
.
,
, and
.
With some substitution, we get and
.