logarithm Model Questions & Answers, Practice Test for ibps clerk prelims 2023
ibps clerk prelims 2023 SYLLABUS WISE SUBJECTS MCQs
Ratio & Proportion
Percentages
Profit & Loss
Time & Work
Time & Distance
Simple Interest & Compound Interest
Mensuration: Area & Volumes
Algebraic Expressions
Trigonometric Ratios & Identity
Linear Equations
Quadratic Equations
Logarithm
What is the value of $2\text"log"(5/8) + \text"log" (128/125) + \text"log" (5/2)$
Answer: (b)
$2 \text"log" (5/8) + \text"log" ({128}/{125}) + \text"log"(5/2)$
= $2 \text"log" 5 - 2 \text"log" 8 + \text"log" 128 - \text"log" 125 + \text"log" 5 - \text"log" 2$
= $2 \text"log" 5 - 2 \text"log"2^3 + \text"log" 2^7 - \text"log"5^3 + \text"log" 5 - \text"log" 2$
=$(2 \text"log" 5 - 6 \text"log" 2) + (7 \text"log" 2 - 3 \text"log" 5) + \text"log" 5 - \text"log" 2$
= $3 \text"log" 5 - 3 \text"log" 5 - 7 \text"log" 2 + 7 \text"log" 2$ = 0
What is the value of $[log_{10} (5 log_{10} 100)]^2$ ?
Answer: (d)
$[log_{10} (5 log_{10} 100)]^2 = [log_{10} (5 log_{10} 10^2)]^2$
= $[log_{10} (10 log_{10} 10)]^2 (∵ log_{10} 10 = 1)$
= $[log_{10} 10]^2$
= $l^2$ = 1
What are the roots of the equation $2^{x + 2} . 27^{x/{x - 1}} = 9$ ?
Answer: (a)
$2^{x + 2} 27^(x/{x - 1})$ = 9
$2^{x+2} 27^(x/{x - 1}) = 2^0 3^2$
$2^{x + 2} = 2^0$
x = – 2
now taking $2^{x+2} , x/{27^{x - 1}}$ = 9
$log[2^{x + 2} 27^(x/{x - 1})] = log 3^2$
(x + 2) log (2) + ${3x}/{x - 1}$ log 3 = 2 log 3
(x + 2) log 2 = $[2 - {3x}/{x - 1}]$ log3
(x + 2) log 2 = $[{- x - 2}/{x - 1}]$ log3
1 – x = ${log 3}/{log 2}$
x = 1 – log $(3/2)$
x = –2 and 1 – log $(3/2)$
What is the value of $[\text"log"_{10} (5\text"log"_{10} 100)]^2$
Answer: (c)
$[\text"log"_{10} (5 \text"log"_{10}100)]^2 = [\text"log"_{10}(5 \text"log"_{10}10^2)]^2$
= $[\text"log"_{10}(10 \text"log"_{10}10)]^2$
= $[\text"log"_{10}10]^2 [∵ \text"log"_{10} 10 = 1] = 1^2 = 1$
Find the value of ${1/2} {\text"log"_10} 25 – 2{\text"log"_10} 3 + {\text"log"_10}$ 18.
Answer: (d)
${1/2} \text"log"_{10} 25 - 2 \text"log"_{10}3 + \text"log"_{10}$ 18
= $\text"log"_{10} (25)^{1/2} - \text"log"_{10} (3)^2 + \text"log"_{10}$ 18
= $\text"log"_{10}5 - \text"log"_{10}9 + \text"log"_{10}$(9 × 2)
= $\text"log"_{10}5 - \text"log"_{10}9 + \text"log"_{10}9 + \text"log"_{10}$2
= $\text"log"_{10}5 + \text"log"_{10}2 = \text"log"_{10} (5 × 2)$
= $\text"log"_{10}$ 10 = 1
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