solve for x

Question

log₄x+log₄(x+2)=log₄3

Answer 1

log_a b  +  log_a c  =  log_a bc 

If log_a b = log_a 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.