Statement-1: If N =((1/0.4))20 then N contains 7 digits before decimal. Statement-2: Characteristic of the logarithm of N to the base 10 is 7 . [Use: log 10 2=0.3010 ]

Question

Statement-1: If N =((1/0.4))20 then N contains 7 digits before decimal. Statement-2: Characteristic of the logarithm of N to the base 10 is 7 . [Use: log 10 2=0.3010 ] (A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1. (B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1. (C) Statement-1 is true, statement-2 is false. (D) Statement-1 is false, statement-2 is true

Tardigrade Admin · Accepted Answer

log 10 N =-20 log 10(4 / 10)=20[1-2 log 10 2]=20[1-2 × 0.301]=20 × 0.398=7.96 ∴ number of digits = characteristic +1=7+1=8 ∴ statement- 1 is false

Q. Statement-1: If $N = (\frac{1}{0.4})^{20}$ then $N$ contains 7 digits before decimal.
Statement-2: Characteristic of the logarithm of $N$ to the base 10 is 7 .
[Use: $lo g_{10} 2 = 0.3010$ ]

Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.

Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.

Statement-1 is true, statement-2 is false.

Statement-1 is false, statement-2 is true

$lo g_{10} N = - 20 lo g_{10} (4/10) = 20 [1 - 2 lo g_{10} 2] = 20 [1 - 2 \times 0.301] = 20 \times 0.398 = 7.96$
$∴$ number of digits $=$ characteristic $+ 1 = 7 + 1 = 8$
$∴$ statement- 1 is false

Q. Statement-1: If N=(0.41​)20 then N contains 7 digits before decimal. Statement-2: Characteristic of the logarithm of N to the base 10 is 7 . [Use: log10​2=0.3010 ]