Logarithm Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

Let m = ${\text"log"_5}^3√5$, then $5^m = ^3√5 = (5)^{1/3}$

So, m = $1/3$. Thus, ${\text"log"_5} ^3√5 = 1/3$ .

Answer: (b)

$2 log (5/8) + log ({128}/{125}) + log (5/2)$

= $log(5/8)^2 + log({128}/{125}) + log(5/2)$

= $log {5^2 × 128 × 5}/{8^2 × 125 × 2} = log {5^2 × 2^7 × 5}/{(2^3)^2 × 5^3 × 2}$

= $log {2^7 × 5^3}/{2^6 × 5^3 × 2} = log {2^7 × 5^3}/{2^7 × 5^3}$ = log 1 = 0

Answer: (a)

${1/3} \text"log"_{10} 125 – 2{\text"log"_{10}} 4 + {\text"log"_{10}} 32 + {\text"log"_{10}}$ 1

=${1/3} \text"log"_{10} (5)^3 – 2{\text"log"_{10}}(2)^2 + {\text"log"_{10}}(2)^5$ + 0

=$\text"log"_{10} 5 – 4{\text"log"_{10}} 2 + 5{\text"log"_{10}2}$

= $\text"log"_{10}5 +\text"log"_{10}2 = \text"log"_{10}10 = 1$

Answer: (a)

$log (108)^{10} = 10 log 108 = 10 log (2^2 × 3^3)$ = 10 (2log2 + 3log3)

= 10 (2 × 0.301 + 3 × 0.477 ) = 10 (.602 + 1.431)

= 10 × 2.033 = 20.33

integral part = 20

No. of digits = 20 + 1 = 21

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

Answer: (a)

$log_{10}(3/2) + log_{10}(4/3) + log_{10}(5/4)+ ..... + 8^{th} term$

= $log_{10}(3/2) + log_{10}(4/3)+ log_{10}(5/4)+ ..... +log_{10}({10}/9)$

= $log_{10}(3/2 × 4/3 × 5/4 ×......× {10}/9)$

= $log_{10}({10}/2)log_{10} 5$.