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log4x+log4(x+2)=log43

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loga b  +  loga c  =  loga bc 

If loga b = loga c , then b = c   
~~~~~~~~~~~ 

log4 x  +  log4 (x + 2)  =  log4 3

log4 x(x + 2)  =  log4 3

x(x + 2) = 3

x2 + 2x - 3 = 0 

(x -1)(x + 3) = 0

x1 = 1 
x2 = - 3 (The  log function is only defined for positive values of the argument)

Thus, x = 1 is the answer.