CAT 1997 — QA Question 9
LogarithmsEasy
Passage / Data
Answer the next 3 questions based on the following information.
There are 60 students in a class. These students are divided into three groups A, B and C of 15, 20 and 25 students each. The groups A and C are combined to form group D.
If log2 [log7 (x2 - x + 37)] = 1, then what could be the value of ‘x’?
Answer & solution
- A
3
- B
5
4
- D
None of these
Solution
We know that if loga x = y , then x = ay . So comparing this form with our equation, we can get log7 (x2 – x + 37) = 21 = 2 and furthermore from this we can say that
(x2 – x + 37) = 72 = 49
Thus, we have the equation
x2 – x – 12 = 0
The solutions of this equations are,
x = 4 or x = –3.
The value that satisfies the given answer-choices is
x = 4.