Answer:
x = 5 or -1
We reject the second answer of x = -1
This is because upon substituting, it will give a negative number which the logarithm value of a negative number is not obtainable
So our only correct answer here is x = 5
Explanation:
From the logarithmic rules;
log a - log b = log (a/b)
Applying this here, we have;
log4(x^2-4/4x+ 1) = 0
(x^2-4)/(4x+ 1) = 4^0
(x^2-4)/(4x + 1) = 1
x^2 -4 = 1(4x + 1)
x^2 -4 = 4x + 1
x^2 - 4x -4-1 = 0
x^2 -4x -5 = 0
x^2+ x -5x -5 = 0
x(x + 1) -5(x + 1) = 0
(x-5)(x + 1) = 0
x = 5 or -1