Question 305765: what is x in this logarithmic equation: log4(x+3)+log4(x-3)=2
Answer by toidayma(44)   (Show Source):
You can put this solution on YOUR website! Condition of x: x + 3 >0 and x - 3 > 0 <-> x > 3
log4(x+3)+log4(x-3)=2 <->
4^(log4(x+3)+log4(x-3)) = 4^2 <->
4^log4(x+3) * 4^log4(x-3) = 16 <->
(x+3)(x-3) = 16 <->
x^2 - 25 = 0 <->
x = 5 or x = -5.
Since x must be larger than 3, therefore x = 5 is the only root of the equation.
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