SOLUTION: log(x+6)+logx=3 solve for x

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: log(x+6)+logx=3 solve for x      Log On


   

Question 396748: log(x+6)+logx=3
solve for x
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use the general formula:
log%28a%29+%2B+log%28b%29+=+log%28a%2Ab%29
log%28x+%2B+6%29+%2B+log%28x%29+=+3
log%28%28x+%2B+6%29%2Ax%29+=+3
I can rewrite this as:
10%5E3+=+x%5E2+%2B+6x
x%5E2+%2B+6x+-+1000+=+0
Using the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+6
c+=+-1000
x+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A1%2A%28-1000%29+%29%29%2F%282%2A1%29+
x+=+%28-6+%2B-+sqrt%2836+%2B+4000%29%29%2F2
x+=+%28-6+%2B+63.53%29%2F2
x+=+28.765 answer
and
x+=+%28-6+-+63.53%29%2F2
x+=+-34.765
This result is impossible, since there is no way that
raising 10 to a power, or log, can give a (-) number
--------------
I'll check the answer:
log%28x+%2B+6%29+%2B+log%28x%29+=+3
log%2828.765+%2B+6%29+%2B+log%2828.765%29+=+3
log%2834.765%29+%2B+log%2828.765%29+=+3
1.541+%2B+1.459+=+3
2.9998+=+3
close enough