SOLUTION: I need help with solving this logarithmic equation log x+log(x+3)=1

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Question 129924: I need help with solving this logarithmic equation
log x+log(x+3)=1
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%2Cx%28x%2B3%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


10%5E%281%29=x%28x%2B3%29 Rewrite the equation using the property: log%28b%2C%28x%29%29=y ====> b%5Ey=x


10=x%28x%2B3%29 Evaluate 10%5E%281%29 to get 10


10=x%5E2%2B3x Distribute


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


0=%28x%2B5%29%28x-2%29 Factor the right 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, if you plug in x=-5, you'll have a negative number in the log.

So our only answer is x=2