SOLUTION: When we have an equation of logarithms how do we work to solve it?(is that the right way or not?)Write a methodology please... for ex: log3x + log(x+5) = log(X^2+4x)/X>0,X d

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Question 8613: When we have an equation of logarithms how do we work to solve it?(is that the right way or not?)Write a methodology please...
for ex:
log3x + log(x+5) = log(X^2+4x)/X>0,X different from 0
Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming your problem is
log%28%283x%29%29+%2B+log%28%28x%2B5%29%29+=+log%28%28x%5E2%2B4x%29%29

Using the second law of logarithms:
log%28%28%283x%29%2A%28x%2B5%29%29%29+=+log%28%28x%5E2%2B4x%29%29

Since the log(M) = log(N) implies that M=N,
3x%28x%2B5%29+=+%28x%5E2+%2B+4x%29
3x%5E2+%2B+15x+=+x%5E2+%2B+4x, which is a quadratic equation.

Set equal to zero,
2x%5E2+%2B+11x+=+0 and solve by factoring:

x(2x+11) = 0
x=0 or x = -11%2F2

However, both answers must be rejected, since you cannot have a log of a negative or zero number. There is NO SOLUTION!!

Does anyone see any errors here?

R^2 at SCC