SOLUTION: Solve 8^(x+8)=32^x

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Question 270985: Solve 8^(x+8)=32^x
Found 2 solutions by drk, Alan3354:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
we start with
8%5E%28x%2B8%29=32%5Ex
step 1 - rewrite as
(ii) 8%5Ex%2A8%5E8+=+32%5Ex
Now 32^x = 8^x*4^x.
step 2 - divide by 8^x to get
(iii) 8%5E8+=+8%5Ex%2A4%5Ex%2F8%5Ex
step 3 - cancel the 8^x to get
(iv) 8%5E8+=+4%5Ex
step 4 - rewrite both as base 2 to a power as
(vii) %282%5E3%29%5E8+=+%282%5E2%29%5Ex
step 5 - use rules of exponents to get
(viii) 2%5E24+=+2%5E2x
step 6 - eliminate the base 2's to get
(ix) 24+=+2x
step 7 - divide by 2 to get
(x) x+=+12

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve 8^(x+8)=32^x
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8 = 2^3; 32 = 2^5
2^(3x+24) = 2^5x
3x+24 = 5x
x = 12