01 Relation & Functions | Find Domain of a Composite Log Function | KT | JEE | CBSE|

📘 Chapter: Relations and Functions
🎯 Exam Focus: KCET | JEE Main | CBSE Class 12
🧮 Question Type: Multiple Choice Question MCQ📌 Question discussed in this video:
The domain of the function
f(x) = log base 4 of (log base 5 of (log base 3 of (18x minus x squared minus 77))) is:
(a) (4, 5) (b) (0, 10) (c) (8, 10) (d) (8, 10]

🧠 Solution

Since log x is defined only when x is greater than 0,
f(x) is defined if log base 5 of (log base 3 of (18x minus x squared minus 77)) is greater than 0.

This means:
log base 3 of (18x minus x squared minus 77) must be greater than 1
which implies:
18x minus x squared minus 77 is greater than 3
so:
18x minus x squared minus 80 is greater than 0

Multiply both sides by -1:
x squared minus 18x plus 80 is less than 0

Factor it:
(x minus 10)(x minus 8) is less than 0

This inequality is satisfied when x is between 8 and 10

✅ Therefore, the domain of the function is: (8, 10)

Correct option: (c) (8, 10)

✅ In this video, we solve a composite logarithmic function domain problem using logical steps and factorisation. This type of question is common in:

Karnataka CET

JEE Main

CBSE final exams

We explain:

Logarithm domain rules

Quadratic inequality using sign method

How to avoid common mistakes in solving

📚 This problem is from the Relations and Functions chapter. This video is part of a larger playlist covering topic-wise problems including:

MCQs

Numerical value type

“Prove that” & “Show that” questions

🎓 Watch till the end to strengthen your concept clarity and problem-solving speed.

🔔 Don’t forget to Like, Subscribe, and Share if you found it useful!
#KCETMaths #JEEMaths #CBSEClass12 #MathDomain #LogFunction #RelationsAndFunctions #MathMCQ #BoardExamMaths #MathTutorial #SrividyaAcademy

Видео 01 Relation & Functions | Find Domain of a Composite Log Function | KT | JEE | CBSE| канала Srividya – CET | JEE | PUC Maths