SOLUTION: Given that 3^-n = 0.2. Find the value of (3^4)^n

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Question 1077519: Given that 3^-n = 0.2.
Find the value of (3^4)^n
Found 2 solutions by MathLover1, math_helper:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Given that
3%5E%28-n%29+=+0.2........solve for n
1%2F3%5En+=+2%2F10
1%2F3%5En+=+1%2F5 =>if nominators same, denominators are same too
3%5En+=+5...........take log of both sides
log%283%5En%29+=+log%285%29
n%2Alog%283%29+=+log%285%29
n+=+log%285%29%2Flog%283%29
n+=+1.46497

Find the value of %283%5E4%29%5En=3%5E%284n%29+:
%283%29%5E%284%2A1.46497%29+=624.99=625

Answer by math_helper(2461) About Me  (Show Source):