SOLUTION: Log4x+log4(x-3)=1 find the solution

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Question 1207158: Log4x+log4(x-3)=1 find the solution
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Sorry, I thought it was -

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
Log4x+log4(x-3)=1 find the solution
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Log4x + log4(x-3) = 1


    Assuming that the logarithms are base 4 . . . 


log%284%2Cx%29 + log%284%2C%28x-3%29%29 = 1  

log%284%2C%28x%2A%28x-3%29%29%29 = 1 
 
x*(x-3) = 4

x%5E2+-+3x+-+4 = 0

Factor left side

(x-4)*(x+1) = 0


Of two roots of the last equation, only x= 4 is the solution to the original equation.

x= -1 does not work, since only positive argument is allowed to logarithm.


ANSWER.  The original equation has a unique solution x= 4 in real numbers.

Solved.