SOLUTION: 3.5 x 7^(4x-1)= 1000^(3-x) find what x equals

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Question 750171: 3.5 x 7^(4x-1)= 1000^(3-x)
find what x equals
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3.5 x 7^(4x-1)= 1000^(3-x)
log(3.5) + (4x-1)*log(7) = (3-x)*log(1000) = (3-x)*3
log(7) - log(2) + (4x-1)*log(7) = 9 - 3x
log(7) - log(2) + 4x*log(7) - log(7) = 9 - 3x
4xlog(7) + 3x = 9 + log(2)
x*(4log(7) + 3) = log(2) + 9
x = (log(2) + 9)/(4log(7) + 3)
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x = (log(2) + log(10^9))/(log2401 + log(1000))
x = log(2E9)/log(2401000)
x =~ 1.457752088