SOLUTION: 27^3n-1 = 81^ -n

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Question 41768: 27^3n-1 = 81^ -n
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
Assuming you mean +27%5E%283n-1%29+=+81%5E%28-n%29+

then we get +3%5E3%5E%283n-1%29+=+3%5E4%5E%28-n%29+
+3%5E%283%283n-1%29%29+=+3%5E%28-4n%29+

and so we have 3 raised to a power on both sides of the equal sign, so the 2 powers must be the same.

--> 3(3n-1) = -4n
9n-3 = -4n
13n = 3
n = 3/13

CHECK:
3n-1 is -4/13
-n is -3/13

so work out if +27%5E%28-4%2F13%29+ is the same as +81%5E%28-3%2F13%29+. Both come to the same decimal.

jon.