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) 1
(b) 10
(c) 3
(d) 0
The correct answers to the above question in:
Answer: (d)
$x log_{10}({10}/3) + log_{10} 3 = log_{10} (2 + 3^x) + x$
$xlog_{10} 10 - x log_{10} 3 + log_{10} 3 = log_{10} (2 + 3^x)$ + x
x - $log_{10^3^x} + log_{10^3} = log_{10} (2 + 3^x)$ + x
$log_{10[3/{3^x}]} log_{10} (2 + 3^x)$
⇒$3^{1–x} = 2 + 3^x$
⇒$3^{1–x} –3^x = 3^1 – 3^0$
x = 0
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Question : 1
The sides of a triangle are 30 cm, 28 cm and 16 cm respectively. In order to determine its area, the logarithm of which of the quantities are required ?
a) 37, 21, 11, 9
b) 37, 11, 28, 16
c) 21, 30, 28, 7
d) 37, 21, 9, 7
Answer »Answer: (d)
Semiperimeter of triangle = ${30 + 16 + 28}/2$ = 37
P – a = 7
P – b = 9
P – c = 21
P = 37
∴ quantities that are required
= 37, 21, 9, 7
Question : 2
What is $log_{10} (3/2) + log_{10} (4/3) + log_{10} (5/4)$ + ..... upto 8 terms equal to?
a) $log_{10}5$
b) 0
c) 1
d) None of these
Answer »Answer: (a)
$log_{10}(3/2) + log_{10}(4/3) + log_{10}(5/4)+ ..... + 8^{th} term$
= $log_{10}(3/2) + log_{10}(4/3)+ log_{10}(5/4)+ ..... +log_{10}({10}/9)$
= $log_{10}(3/2 × 4/3 × 5/4 ×......× {10}/9)$
= $log_{10}({10}/2)log_{10} 5$.
Question : 3
If ${\text"log"_8} x + {\text"log"_8} {1/6} = 1/3$, then find the value of x.
a) 16
b) 18
c) 12
d) 24
e) None of these
Answer »Answer: (c)
${\text"log"_8}x +{ \text"log"_8} {1/6} = 1/3$
or ${\text"log"_8} (x × {1/6}) = 1/3 or {\text"log"_8} (x/6) = 1/3$
or $x/6 = (8)^{1/3}$ {∵ $\text"log"_a$ b = x⇔(a)x=b}
or ${x/6} = (2^3)^{1/3}$ or x = 12
Question : 4
If ${\text"log"_a} b = 1/2, {\text"log"_b}$ c = $1/3$ and ${\text"log"_c}$ a = $k/5$, then the value of k is
a) 30
b) 25
c) 20
d) 35
e) None of these
Answer »Answer: (a)
${\text"log"_a} b = {1/2}, {\text"log"_b}c= {1/3}$, and ${\text"log"_c} a = k/5$
⇒${\text"log" b}/{\text"log" a} = {1/2}, {\text"log" c}/{\text"log" b} = {1/3}, {\text"log" a}/{\text"log" c} = k/5$
⇒${1/2} × {1/3} × {k/5}$ = 1⇒k = 30
Question : 5
If a = $\text"log"_{24} 12, b = \text"log"_{36}$ 24, C = $\text"log"_{48}$ 36. Then 1 + abc is equal to
a) 2ab
b) 2ac
c) 2abc
d) 2bc
e) None of these
Answer »Answer: (d)
abc = ${\text"log" 12}/{\text"log" 24} . {\text"log" 24}/{\text"log" 36} . {\text"log" 36}/{\text"log" 48} = {\text"log" 12}/{\text"log" 48}$
∴ 1 + abc = ${\text"log" 48 + \text"log"12}/{\text"log" 48} = {\text"log" (48.12)}/{\text"log" 48}$
= ${\text"log"24}^2/{\text"log" 48} = 2.{\text"log" 24}/{\text"log" 48}$ = 2bc
Question : 6
If log x = 1.2500 and y = $x^{logx}$ , then what is log y equal to?
a) 1.5625
b) 4.2500
c) 2.5625
d) 1.2500
Answer »Answer: (a)
We have, y = $x^{logx}$
Taking log on both sides log
y = log $(x^{logx})$
= logx. logx = $(1.25)^2$ = 1.5625
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