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The domain of the definition of the function $f (x) = \log_{4} (\log_{5} (\log_{3} (18 x - x^{2} - 77))) is$

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x∈(12,20)

x∈(8,10)

x∈(20,25)

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Correct option is B

Since log⁡x is defined for x>0 . Therefore, for f(x)=log4⁡log5⁡log3⁡18x−x2−77log5⁡log3⁡18x−x2−77>0⇒log3⁡18x−x2−77>50⇒18x−x2−77>31⇒ x2−18x+80<0⇒ (x−8)(x−10)<0⇒ 8

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The domain of the definition of the function f(x)=log4⁡log5⁡log3⁡18x−x2−77 is

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The domain of the definition of the function $f (x) = \log_{4} (\log_{5} (\log_{3} (18 x - x^{2} - 77))) is$