Log(x+2)+log(x-2)=log5 . Find the value of" x"

Question

Logarithm question find the value of x

Answer 1

LOG ( (x+2)(x-2)) = log 5

 

 (x+2)(x-2) = 5

 

x^2 - 4 = 5

 

 x^2 - 9 = 0

 

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

 

 x= -3 or x = 3

 

The solution x=-3 results in the log of a negative number,

 and negative numbers are NOT in the domain of the log function.

 

The solution x=3 checks out!  log(3+2) + log (3-2) = log(5) + log(1) = log(5) + 0 = log(5)

 

So x=3