Posted by Lucy on Monday, March 17, 2008 at 6:28pm.
the key is to recognize
both 81 and 243 as powers of 3
81 = 3^4 and 243 = 3^5
so (1/81)^t=243^t-2
(3^-4)^t = (3^5)^(t-2)
3^(-4t) = 3^(5t-10)
then -4t = 5t - 10
-9t=-10
t=10/9
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