SOLUTION: To expand the logarithmic expression as much as possible: In x^3/(x-3)^2 Solve: log10 (x-30)= 3- log10 x

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: To expand the logarithmic expression as much as possible: In x^3/(x-3)^2 Solve: log10 (x-30)= 3- log10 x       Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 4867: To expand the logarithmic expression as much as possible:
In x^3/(x-3)^2
Solve:
log10 (x-30)= 3- log10 x

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
i take it you mean ln+%28x%5E3%2F%28x-3%29%5E2%29? If so, it becomes

ln%28x%5E3%29+-+ln%28x-3%29%5E2
3ln%28x%29+-+2ln%28x-3%29

solve log10+%28x-30%29=+3-+log10+x..I shall leave out the base, for ease of reading --> log%28x-30%29=+3+-+log%28x%29.

log%28x-30%29+%2B+log%28x%29+=+3
log%28x%28x-30%29%29+=+3
log%28x%5E2-30x%29+=+3
x%5E2-30x+=+10%5E3
x%5E2-30x+=+1000
x%5E2-30x-1000+=+0
(x+20)(x-50) = 0

so x+20 = 0 OR x-50=0

so, x=-20 or x=50

in terms of logs, you cannot have negatives, so x=-20 will not be allowed, so x=50 is your one and only answer.

jon