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

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

Answer: (a)

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

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

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

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

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)

${\text"log"_a} b = {1/2}, {\text"log"_b}c= {1/3}$, 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

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

Answer: (a)

We have, y = $x^{logx}$

Taking log on both sides log

y = log $(x^{logx})$

= logx. logx = $(1.25)^2$ = 1.5625