What is the domain of f(x)=log_{5}(x^2-4x+1)^x ?

The domain of f(x)=log_{5}(x^2-4x+1)^x is x = 4

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domain of f(x)=log_{5}(x^2-4x+1)^x

domain

f (x) = lo g_{5} (x^{2} - 4 x + 1)^{x}

x < 0 or x \geq 4

Interval Notation

(- \infty, 0) \cup [4, \infty)

Solution steps

Find positive values for logs:

x < - 3 + 2 or x > 3 + 2

Check exponents domain:

x < 0 or x \geq 4

Combine real regions and undefined points for final function domain

x < 0 or x \geq 4

What is the domain of f(x)=log_{5}(x^2-4x+1)^x ?
The domain of f(x)=log_{5}(x^2-4x+1)^x is x<0\lor x>= 4