The domain of the function f(x)=log10⁡1−log10⁡x2−5x+16 is

f (x) is defined if1−log10⁡x2−5x+16>0 and x2−5x+16>0⇒log10⁡x2−5x+16<1 and x−522+394>0⇒x2−5x+16<101=10 ∵x−522+394>0 for all real x⇒ x2 – 5x + 6 < 0⇒ (x – 3) (x – 2) < 0 ⇒ 2 < x < 3∴Domain of f = (2, 3)