logarithm Model Questions & Answers, Practice Test for ibps clerk prelims 2023

Answer: (b)

Answer: (c)

$log_{100}(0.72) = log_{100}({72}/{100})$

= $log_{100}72 – log_{100}100 = log_{100}(8 × 9) – 1$

= $log_{100}(2^3 × 3^2) – 1 = log_{(10)^2} 2^3 + log_{(10)^2} (3^2) - 1$

= $3/2 log_{10} 2 + 2/2 log_{10} 3 - 1 = \ov{1}.9286$

Answer: (c)

$1/5 log_{10} 3125 - 4 log_{10}2 + log_{10} 32$

= $1/5 log_{10}(5)^5 - 4 log_{10}2 + log_{10}(2)^5$

= $5/5 log_{10} 5 - 4 log_{10} 2 + 5 log_{10} 2 = log_{10} 5 + log_{10} 2$

= $log_{10}$ (5 × 2)

[log m + log n = log mn]

= $log_{10}$ 10 = 1

∴ Option (c) is correct.

Answer: (c)

Given expression = ${1/{{\text"log xyz"}/{\text"log xy"}} + {1/{{\text"log xyz"}/{\text"log yz"}} + {1/{{\text"log xyz"}/{\text"log zx"}}$

${\text"log xy" + \text"log yz" + \text"log zx"}/{\text"log xyz"} = {\text"log" x^2 y^2 z^2}/{\text"log xyz"}$

${2 \text"log xyz"}/{\text"log xyz"}$ = 2

Answer: (a)

A = $\text"log"_2 \text"log"_2 \text"log"_4 (4)^4 + 2\text"log"_{√2}(√2)^2$

= $\text"log"_2 \text"log"_2 4 + 2 × 2$ ∵ $\text"log"_a$ a = l

=$\text"log"_2 \text"log"_2(2)^2 + 4$ = $\text"log"_2 2 +4 = 1+4 = 5$