log_{4}x+log_{4}(x+2)=log_{4}3
log_{a} b + log_{a} c = log_{a} bc
If log_{a} b = log_{a} c , then b = c
~~~~~~~~~~~
log_{4} x + log_{4} (x + 2) = log_{4} 3
log_{4} x(x + 2) = log_{4} 3
x(x + 2) = 3
x^{2} + 2x - 3 = 0
(x -1)(x + 3) = 0
x_{1} = 1
x_{2} = - 3 (The log function is only defined for positive values of the argument)
Thus, x = 1 is the answer.
If log_{a} b = log_{a} c , then b = c
~~~~~~~~~~~
log_{4} x + log_{4} (x + 2) = log_{4} 3
log_{4} x(x + 2) = log_{4} 3
x(x + 2) = 3
x^{2} + 2x - 3 = 0
(x -1)(x + 3) = 0
x_{1} = 1
x_{2} = - 3 (The log function is only defined for positive values of the argument)
Thus, x = 1 is the answer.