Question
The value of \({\log _a}\left( {\frac{a}{b}} \right) + {\log _b}\left( {\frac{b}{a}} \right),\) for \(1 < a \le b\) cannot be equal to
- -0.5
- 1
- 0
- -1
Option: 2
Solution:
Solution:
\({\log _a}\left( {\frac{a}{b}} \right) + {\log _b}\left( {\frac{b}{a}} \right)\)
\( = {\log _a}a - {\log _a}b + {\log _b}b - {\log _b}a\)
\( = 1 - {\log _a}b + 1 - {\log _b}a\quad \left[ {{{\log }_n}n = 1} \right]\)
since \(\left( {{{\log }_a}b + {{\log }_a}b} \right) \ge 2\)
\(\therefore \) The above value is \( \le 0\).
\(\therefore 1\) can't be the answer.
CAT 2020 Quant questions with Solutions
- CAT 2020 Quant Question 1
- CAT 2020 Quant Question 2
- CAT 2020 Quant Question 3
- CAT 2020 Quant Question 4
- CAT 2020 Quant Question 5
- CAT 2020 Quant Question 6
- CAT 2020 Quant Question 7
- CAT 2020 Quant Question 8
- CAT 2020 Quant Question 9
- CAT 2020 Quant Question 10
- CAT 2020 Quant Question 11
- CAT 2020 Quant Question 12
- CAT 2020 Quant Question 13
- CAT 2020 Quant Question 14
- CAT 2020 Quant Question 15
- CAT 2020 Quant Question 16
- CAT 2020 Quant Question 17
- CAT 2020 Quant Question 18
- CAT 2020 Quant Question 19
- CAT 2020 Quant Question 20
- CAT 2020 Quant Question 21
- CAT 2020 Quant Question 22
- CAT 2020 Quant Question 23
- CAT 2020 Quant Question 24
- CAT 2020 Quant Question 25
- CAT 2020 Quant Question 26
- CAT 2020 Quant Question 27
- CAT 2020 Quant Question 28
- CAT 2020 Quant Question 29
- CAT 2020 Quant Question 30
- CAT 2020 Quant Question 31
- CAT 2020 Quant Question 32
- CAT 2020 Quant Question 33
- CAT 2020 Quant Question 34
- CAT 2020 Quant Question 35
- CAT 2020 Quant Question 36
- CAT 2020 Quant Question 37
- CAT 2020 Quant Question 38
- CAT 2020 Quant Question 39
- CAT 2020 Quant Question 40
- CAT 2020 Quant Question 41
- CAT 2020 Quant Question 42
- CAT 2020 Quant Question 43
- CAT 2020 Quant Question 44
- CAT 2020 Quant Question 45
- CAT 2020 Quant Question 46
- CAT 2020 Quant Question 47
- CAT 2020 Quant Question 48
- CAT 2020 Quant Question 49
- CAT 2020 Quant Question 50
- CAT 2020 Quant Question 51
- CAT 2020 Quant Question 52
- CAT 2020 Quant Question 53
- CAT 2020 Quant Question 54
- CAT 2020 Quant Question 55
- CAT 2020 Quant Question 56
- CAT 2020 Quant Question 57
- CAT 2020 Quant Question 58
- CAT 2020 Quant Question 59
- CAT 2020 Quant Question 60
- CAT 2020 Quant Question 61
- CAT 2020 Quant Question 62
- CAT 2020 Quant Question 63
- CAT 2020 Quant Question 64
- CAT 2020 Quant Question 65
- CAT 2020 Quant Question 66
- CAT 2020 Quant Question 67
- CAT 2020 Quant Question 68
- CAT 2020 Quant Question 69
- CAT 2020 Quant Question 70
- CAT 2020 Quant Question 71
- CAT 2020 Quant Question 72
- CAT 2020 Quant Question 73
- CAT 2020 Quant Question 74
- CAT 2020 Quant Question 75
- CAT 2020 Quant Question 76
- CAT 2020 Quant Question 77
- CAT 2020 Quant Question 78