SOLUTION: I having trouble solving this equation log (x+3)=1-log x

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Question 56747: I having trouble solving this equation
log (x+3)=1-log x
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
The rules we are going to use are:
highlight%28log%28a%29%2Blog%28b%29=log%28a%2Ab%29%29
highlight%28log%28a%29=m%29==>>highlight%2810%5Em=a%29
log%28%28x%2B3%29%29=1-log%28%28x%29%29
log%28%28x%29%29%2Blog%28%28x%2B3%29%29=1-log%28%28x%29%29%2Blog%28%28x%29%29
log%28%28x%29%29%2Blog%28%28x%2B3%29%29=1
log%28x%28x%2B3%29%29=1
10%5E1=x%28x%2B3%29
10=x%5E2%2B3x
-10%2B10=x%5E2%2B3x-10
0=x%5E2%2B3x-10 Factor:
0=(x__)(x___)
We need to fill the blanks with two integers that multiply to give us:-10, but add to give us:+3
5*(-2)=-10 and 5-2=+3
0=(x+5)(x-2)
x+5=0 and x-2=0
x=-5 and x=2
We have to check for extraneous solutions:
log%28-5%2B3%29=1-log%28-5%29 x=-5 is extraneous, because we can't take the log of a negative number.
log%282%2B3%29=1-log%282%29
log%285%29=1-log%282%29
.6989700043=.698700043
x=2 is a solution.
Happy Calculating!!!