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

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

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: (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

Answer: (d)

$(\text"log"_{1/2}2)(\text"log"_{1/3}3)(\text"log"_{1/4}4).......(\text"log"_{1/{1000}}1000)$

=$({\text"log" 2}/{\text"log"{1/2}})({\text"log" 3}/{\text"log"{1/3}})({\text"log" 4}/{\text"log"{1/4}})......({\text"log" 1000}/{\text"log"{1/{1000}}})$ $(∵ \text"log"_b a = {\text"log" a}/{\text"log" b})$

= $({\text"log" 2}/{- \text"log" 2})({\text"log" 3}/{-\text"log" 3})({\text"log" 4}/{-\text"log" 4}) ...... ({\text"log" 1000}/{\text"log" 1000})$

= (-1) × (-1) × (-1) × .....× (-1)

(∵ number of terms is odd) = -1