MCQ: लॉगरिदम - 2 - Bank Exams MCQ

आवश्यक उत्तर = [64 लॉग₁₀ 2] + 1
= [ 64 x 0.3010 ] + 1
= 19.264 + 1
= 19 + 1
= 20

दिया गया Exp.= log₂3 x log₃2 x log₃4 x log₄3
= (log3 / log2) x ( log2 / log3) x (log4 / log3) x (log3 / log4) = 1 

दी गई अभिव्यक्ति = log [{(9/8) / (27/32)} x 3/4]
= log [(9/8) x (3/4) x (32/27)]
= log 1
= 0

∵ log_a x = ( log_abx) / (log_aba)
∴ दिए गए अभिव्यक्ति = [[(log_abx) / (log_aba)] / [( log_abx )] - ( log_ab)
= (1/log_aba) - log_ab = log_aab - log_ab = log_a(ab/b)
= log_aa = 1 

log₂ 10 = log 10 / log 2
= 1 / log 2
= 1.0000 / 0.3010
= 1000 / 301 

= log(75/16) - 2 log(5/9) + log(32/243)
= log [(25 x 3) / (4 x 4)] - log (25/81) + log [(16 x 2) / (81 x 3)]
= log(25 x 3) - log (4 x 4) - log(25) + log(81) + log(16 x 2) - log (81 x 3)
= log 25 + log 3 - log 16 - log 25 + log 81 + log 16 + log 2 - log 81 - log 3
= log 2 

log₁₀2.8 = log₁₀(28/10)
= log 28 - log 10
= log (7 x 4) - log 10
= log 7 + 2 log 2 - log 10
= 0.8451 + 2 x 0.3010 - 1
= 0.8451 + 0.6020 - 1
= 0.4471 

दी गई व्यंजक: log (a² / bc) + log (b² / ac) + log (c² / ab)
= log [(a² x b² x c²) / (abc)]
= log 1
= 0 

लॉग 5 = लॉग 10 / 2 = लॉग 10 - लॉग 2
= 1 - 0.3010 = 0.6990

log₁₀50 = log₁₀[(50 x 2) / 2]
= log 100 - log 2
= log₁₀10² - log 2
= 2 - 0.301
= 1.699 

दी गई अभिव्यक्ति = लॉग 8 + लॉग (1/8)
= लॉग 8 x (1/8)
= लॉग 1
= 0

दिया गया अभिव्यक्ति = log x + log (1/x)
= log x + log 1 - log x
= log 1
= 0

∵ 2log₄x = 1 + log₄(x-1)
⇒ log₄x² = log₄4 + log₄(x-1)
⇒ x² = 4(x-1)
⇒ x² - 4x + 4 = 0
⇒ (x-2)² = 0
∴ x = 2 

log_ax + log_a(1+x) = 0
⇒ log_ax (x+1) = log_a1 (क्योंकि log 1 = 0)
⇒ x(x +1) = 1
∴ x² + x - 1 = 0 

दिया गया है लॉग 90 = 1.9542
⇒ लॉग(3² x 10) = 1.9542
⇒ 2लॉग 3 + लॉग 10 = 1.9542
∴ लॉग 3 = 0.9542 / 2 = 0.4771