SOLUTION: I need to solve this equation on a worksheet: log X +log (X + 2) = log 3 Thank you!!!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I need to solve this equation on a worksheet: log X +log (X + 2) = log 3 Thank you!!!      Log On


   

Question 70987: I need to solve this equation on a worksheet:
log X +log (X + 2) = log 3
Thank you!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log+X+%2Blog+%28X+%2B+2%29+=+log+3
log%28x%5E2%2B2x%29=log+3Combine logs using basic identity log(x)+log(y)=log(x*y)
cross%2810%29%5E%28log%28x%5E2%2B2x%29%29=cross%2810%29%5E%28log+3%29Cancel out logs by making the base 10 with the equation as a raised power (which undoes the logs with base 10)
x%5E2%2B2x=3Now you have an equation in which you can solve for x
%28x-1%29%28x%2B3%29=0Get everything to one side and factor it, then solve for x
x=1 and x=-3 are your solutions. But wait, we're not done yet. We need to check these answers
Check:
Let x=1
log+%281%29%2B+log+%283%29=log+3
log+%281%2A3%29+=+log+3
log+3=+log+3 Answer works
Let x=-3
log+%28%28-3%29%29+%2B+log+%28%28-3%2B2%29%29=log+3 You cannot take the log of a negative number (if you want a real number) so this solution does not work.
So the the only solution that works is x=1