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

Answer: (a)

$\text"log"_{6} 216 √6 = \text"log"_6 (6)^3 (6)^{1/2}$

= $\text"log"_6 (6)^{7/2} = {7/2}{ \text"log"_6} 6 = 7/2$ (∵ $\text"log"_a$ a = 1)

Answer: (d)

$log 7^{25}$ = 25 log 7 = 25 × 0.845

= 21.125

Its characteristic is 21⇒No. of digits = 22

$log 8^{23} = log 2^{69}$ = 69 log 2

= 69 × 0.301 = 20.769

Its characteristic is 20⇒No. of digits = 21

$log 9^{20} = log 3^{40}$

= 40 × log3

= 40 × 0.477 = 19.08⇒No. of digits = 20

Near about is 22, 21, 20 so option (d) satisfy

Answer: (c)

${log_{13}(10)}/{log_{169}(10)} = {log_{13}(10)}/{log_{13^2}(10)}$

$(∵ log_{a^b} c = 1/b log_a c)$

= ${log_{13}10}/{1/2 log_{13}10} = 1/{1/2}$ = 2

Answer: (c)

let $2^{40} = 10^x$

log $2^{40} = log 10^x$

40 $log^2 = x log^{10}$

40 (.301) = x

12.04 = x

i.e. x > 12

∴ x = 13

No. of digit in $2^{40}$ is 13

Answer: (a)

Let $log_{10}$ 0.0001 = a

a = $log_{10} {1/{(10)^4}$

= $log_{10} 1 – log_{10} (10)^4$ = 0 – 4 = –4

Answer: (b)

$log_{10} 1050 = log_{10}$(3 × 10 × 35)

= $log_{10} 3 + 1 + log_{10} 35$

⇒ 3.0212 = $log_{10} 3 + 1 + 1.5441$

⇒$log_{10} 3$ = 0.4771

Now, $log_{10} 35 = log {7 × 10}/2$

= $log_{10} 7 + log_{10} - log_{10} 2$

⇒ $log_{10}7$ = 0.8451

Now, A = ${√3}/4 × (7)^2$

$log{10^A^4} = 4 log_{10}A$

= 4 log ${√3 × 7^2}/4$

= $4[1/2 log_3 + 2 log_{10} 7 - 2 log 2]$ = 5.3070