SOLUTION: Given that 4^-n = 32. Find the value of n

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Question 1132096: Given that 4^-n = 32.
Find the value of n
Found 2 solutions by Edwin McCravy, Alan3354:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
4-n = 32

Write 4 as 22 and 32 as 25

(22)-n = 25

Multiply the exponents on the left to remove the
parentheses:

2-2n = 25

Since the bases on both sides are the same, and 
are different from 1, the exponents must be
equal also, so we set them equal:

-2n = 5

  n = -5/2

Edwin

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Given that 4^-n = 32.
Find the value of n
=========
Find the log of each side.
log%284%5E%28-n%29%29+=+log%2832%29
-n*log(4) = log(32)
n = -log(32)/log(4)
n = -2.5
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Edwin's approach is simpler, but could not be used if the problem were:
Given that 4^-n = 33.
Find the value of n