SOLUTION: log(x-30)=3-logx

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Question 629966: log(x-30)=3-logx
Answer by Charles3475(23) About Me  (Show Source):
You can put this solution on YOUR website!
log(x-30)=3-logx

10%5Elog%28x-30%29+=+10%5E%283-log%28x%29%29 (make both Side Exponents of 10)

10%5Elog%28x-30%29+=+%2810%5E3%29%2F%2810%5Elog%28x%29%29 (10^(a-b) = 10^a/10^b)

%28x-30%29+=+1000%2Fx (simplify 10^log(a) = a)

x%5E2-30%2Ax+=+1000 (multiply both sides by x)

x%5E2+-30x+-1000+=+0 (subtract 1000 from both sides)

%28x-50%29%2A%28x%2B20%29+=+0 (Factor quadratic)

Either (x-50) = 0 or (x+20) = 0

x = 50 or x = -20 (solve)

However, x = -20 is an invalid solution as you can's take the log of a negative number.

x = 50 (answer)