SOLUTION: logx + log(x + 3) = 1 Can someone show me the steps to get the answer of x= -5 or 2? Thanks

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: logx + log(x + 3) = 1 Can someone show me the steps to get the answer of x= -5 or 2? Thanks      Log On

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Question 133332: logx + log(x + 3) = 1
Can someone show me the steps to get the answer of x= -5 or 2?
Thanks
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
log%2810%2C%28x%29%29%2Blog%2810%2C%28x%2B3%29%29=1 Start with the given equation


log%2810%2C%28x%28x%2B3%29%29%29=1 Combine the logs using the identity log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29=log%28b%2C%28A%2AB%29%29


log%2810%2C%28x%5E2%2B3x%29%29=1 Distribute


10%5E%28log%2810%2C%28x%5E2%2B3x%29%29%29=10%5E1 Raise both sides as exponents with bases of 10. This eliminates the logs


x%5E2%2B3x=10 Simplify


x%5E2%2B3x-10=0 Subtract 10 from both sides.



%28x%2B5%29%28x-2%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x%2B5=0 or x-2=0

x=-5 or x=2 Now solve for x in each case


So our possible answers are

x=-5 or x=2



However, since you cannot take the log of a negative number, the only solution is x=2


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Answer:
So our answer is x=2