SOLUTION: how would you solve: log(x+1)+(x-7)=log(10x+10) this is what i did so far: a. log(x+1)(x-7)=log(10x+10) b.log (x+1)(x+7)/(10x+10)---> is this correct...now am stuck i don't kn

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: how would you solve: log(x+1)+(x-7)=log(10x+10) this is what i did so far: a. log(x+1)(x-7)=log(10x+10) b.log (x+1)(x+7)/(10x+10)---> is this correct...now am stuck i don't kn      Log On


   



Question 695513: how would you solve:
log(x+1)+(x-7)=log(10x+10)
this is what i did so far:
a. log(x+1)(x-7)=log(10x+10)
b.log (x+1)(x+7)/(10x+10)---> is this correct...now am stuck i don't know the next step or if i even did it correctly
Thank you in advance!

Found 2 solutions by mouk, MathTherapy:
Answer by mouk(232) About Me  (Show Source):
You can put this solution on YOUR website!
You are correct upto (a)
If +log%28%28x%2B1%29%28x-7%29%29=log%2810x%2B10%29+ then
+%28x%2B1%29%28x-7%29+=+10x%2B10+ because +logA=logB+ if and only if +A=B+
which reduces to a quadratic:
+x%5E2-6x-7=10x%2B10+
+x%5E2-16x-17+=+0+
+%28x-17%29%28x%2B1%29+=+0 so +x=-1+ or +x=17+

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
how would you solve:
log(x+1)+(x-7)=log(10x+10)
this is what i did so far:
a. log(x+1)(x-7)=log(10x+10)
b.log (x+1)(x+7)/(10x+10)---> is this correct...now am stuck i don't know the next step or if i even did it correctly
Thank you in advance!

Is this log+%28%28x+%2B+1%29%2B%28x+-+7%29%29+=+log+%28%2810x+%2B+10%29%29, or is it: log+%28%28x+%2B+1%29%29%2B+log+%28%28x+-+7%29%29+=+log+%28%2810x+%2B+10%29%29?

If it's the latter, then we have: log+%28%28x+%2B+1%29%28x+-+7%29%29+=+log+%28%2810x+%2B+10%29%29

Since this actually means: log+%2810%2C%28x+%2B+1%29%28x+-+7%29%29+=+log+%2810%2C+%2810x+%2B+10%29%29, then: x%5E2+-+6x+-+7+=+10x+%2B+10

x%5E2+-+6x+-+10x+-+7+-+10+=+0

x%5E2+-+16x+-+17+=+0

(x + 1)(x - 17) = 0

x = - 1 (ignore as log+%28%28x+-+1%29%29 CANNOT BE = 0, NOR CAN log+%28%28x+-+7%29%29 BE < 0)

Therefore, only solution is: highlight_green%28x+=+17%29

You can do the check!!

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