Logarithm Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts

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: (d)

Let y = $(0.2)^{25}$

Talking log on both sides, we got

log(y) = $(0.2)^{25}$ = 25. log(0.2)

= 25 $(log (2/{10}))$ = 25 (log2 – log10)

= 25 (0.330103 – 1) = –17.47475

Hence, n = 17

Answer: (a)

Let x = $2^{56}$

⇒$\text"log" x = 56 \text"log" 2$ = 56 × 0.30103 = 16.85

∴ Number of digits in $2^{56}$ = 17