The domain of the function f(x)=log4(log5 (log3(18x-x2-77))) ldots is

Question

The domain of the function f(x)=log4(log5 (log3(18x-x2-77))) ldots is (A) x ∈ (4, 5) (B) x ∈ (0, 10) (C) x ∈ (8, 10) (D) x ∈ (8, 10]

Tardigrade Admin · Accepted Answer

Since log x is defined ∀ x > 0 f(x)=log4(log5 (log3(18x-x2-77))) ⇒ log5(log3(18x-x2-77)) > 0 ⇒ log3(18x-x2-77) > 5° ⇒ log3(18x-x2-77) > 1 ⇒ 18x-x2 -77 > 31 ⇒ (x-8)(x-10) < 0 ⇒ 8 < x < 10 ∴ x ∈(8, 10)

Q. The domain of the function
$f (x) = l o g_{4} (l o g_{5} (l o g_{3} (18 x - x^{2} - 77))) \dots$ is

$x \in (4, 5)$

$x \in (0, 10)$

$x \in (8, 10)$

$x \in (8, 10]$

Q. The domain of the function f(x)=log4​(log5​(log3​(18x−x2−77)))… is

x∈(4,5)

x∈(0,10)

x∈(8,10)

x∈(8,10]

Since logx is defined ∀x>0 f(x)=log4​(log5​(log3​(18x−x2−77))) ⇒log5​(log3​(18x−x2−77))>0 ⇒log3​(18x−x2−77)>5∘ ⇒log3​(18x−x2−77)>1 ⇒18x−x2−77>31 ⇒(x−8)(x−10)<0 ⇒8<x<10 ∴x∈(8,10)

Q. The domain of the function
$f (x) = l o g_{4} (l o g_{5} (l o g_{3} (18 x - x^{2} - 77))) \dots$ is

$x \in (4, 5)$

$x \in (0, 10)$

$x \in (8, 10)$

$x \in (8, 10]$