SOLUTION: If log_8 3=x and log_4 7=y, find an expression in terms of x and y for: 1) log_2 63

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Question 174789: If log_8 3=x and log_4 7=y, find an expression in terms of x and y for:
1) log_2 63
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
log%288%2C3%29+=+x
log%284%2C7%29+=+y
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rewrite these as:
(1) 8%5Ex+=+3
(2) 4%5Ey+=+7
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The problem asks
log%282%2C63%29=z what is z?
rewrite as:
(3) 2%5Ez+=+63
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(1) 8%5Ex+=+3
2%5E%283x%29+=+3
(2) 4%5Ey+=+7
2%5E%282y%29+=+7
-----------------
Now I can write:
2%5E%282y%29+%2A2%5E%283x%29%2A2%5E%283x%29+=+2%5Ez
2%5E%282y+%2B+6x%29+=+2%5Ez
z+=+2y+%2B+6x answer
check answer:
(3) 2%5Ez+=+63
2%5E%282y+%2B+6x%29+=+63
2%5E%282y%29%2A2%5E%286x%29+=+63
2%5E%282y%29%2A2%5E%283x%29%2A2%5E%283x%29+=+63
7%2A3%2A3+=+63
OK