Logarithm Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 1 EXERCISES
The following question based on Logarithm topic of quantitative aptitude
(a) 7/2
(b) 3
(c) 2/7
(d) 3/2
e) None of these
The correct answers to the above question in:
Answer: (a)
$\text"log"_{6} 216 √6 = \text"log"_6 (6)^3 (6)^{1/2}$
= $\text"log"_6 (6)^{7/2} = {7/2}{ \text"log"_6} 6 = 7/2$ (∵ $\text"log"_a$ a = 1)
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Question : 1
What is the number of digits in $7^{25}, 8^{23} and 9^{20}$ respectively ? [Given $log_{10}2 = 0.301, log_{10}3 = 0.477, log_{10}7 = 0.845$]
a) 22, 21, 20
b) 21, 20, 19
c) 20, 19, 18
d) 22, 20, 21
Answer »Answer: (d)
$log 7^{25}$ = 25 log 7 = 25 × 0.845
= 21.125
Its characteristic is 21⇒No. of digits = 22
$log 8^{23} = log 2^{69}$ = 69 log 2
= 69 × 0.301 = 20.769
Its characteristic is 20⇒No. of digits = 21
$log 9^{20} = log 3^{40}$
= 40 × log3
= 40 × 0.477 = 19.08⇒No. of digits = 20
Near about is 22, 21, 20 so option (d) satisfy
Question : 2
What is the value of ${[log_{13}(10)]}/{[log_{169}(10)]}$
a) 1
b) $1/2$
c) 2
d) $log_{10}13$
Answer »Answer: (c)
${log_{13}(10)}/{log_{169}(10)} = {log_{13}(10)}/{log_{13^2}(10)}$
$(∵ log_{a^b} c = 1/b log_a c)$
= ${log_{13}10}/{1/2 log_{13}10} = 1/{1/2}$ = 2
Question : 3
Two packs of cards are thoroughly mixed and shuffled and two cards are drawn at random, one after the other. What is the probability that both of them are jacks?
a) $2/13$
b) $1/169$
c) $1/13$
d) $7/1339$
e) $1/179$
Answer »Answer: (d)
Total number of cards = 104 = 2 × 52
and total number of jacks = 8 = 2 × 4
∴ Probability for the jack in first draw = $8/{104}$
and probability for the jack in second draw = $7/{103}$
Since both the events are independent events.
Hence the probability that both of them are jacks.
= ${8}/{104}$ × ${7}/{103}$ = $7/{1339}$
Question : 4
If ${\text"log"_7}{\text"log"_5} (√x + 5 + √x)$ = 0 , find the value of x.
a) 2
b) 1
c) – 2
d) 0
e) None of these
Answer »Answer: (d)
$\text"log"_7 \text"log"_5(√x + 5 + √x)$ = 0
use $\text"log"_a$ x = b⇒$a^b$=x
∴ $\text"log"_5 (√x + 5 + √x) = 7^0$ = 1
$√x + 5 + √ x = 5^1 = 5⇒2√x$ = 0
∴ x = 0
Question : 5
What is the number of digits in $2^{40}$ ? (Given that $log_{10} 2$ = 0.301)
a) 12
b) 14
c) 13
d) 11
Answer »Answer: (c)
let $2^{40} = 10^x$
log $2^{40} = log 10^x$
40 $log^2 = x log^{10}$
40 (.301) = x
12.04 = x
i.e. x > 12
∴ x = 13
No. of digit in $2^{40}$ is 13
Question : 6
What is the logarithm of 0.0001 with respect to base 10?
a) –4
b) 4
c) 3
d) –3
Answer »Answer: (a)
Let $log_{10}$ 0.0001 = a
a = $log_{10} {1/{(10)^4}$
= $log_{10} 1 – log_{10} (10)^4$ = 0 – 4 = –4
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