∵ 10^x = 1730/1000
∴ log10^x= log₁₀1730 - log₁₀1000

Correct Option: B

∵ 10^x = 1730/1000
∴ log10^x= log₁₀1730 - log₁₀1000
⇒ x = 3.2380 - 3
= 0.2380

log_an / log_abn = [( log n / log a) / (log n / log (a.b))]
= log (a.b) / log a
= ( log a + log b) / log a
= 1 + (log b / log a)

Correct Option: A

log_an / log_abn = [( log n / log a) / (log n / log (a.b))]
= log (a.b) / log a
= ( log a + log b) / log a
= 1 + (log b / log a)
= 1 + log_ab

log_ax + log_a(1+x) = 0
⇒ log_ax (x+1) = log_a1 (since log 1 = 0)

Correct Option: A

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

∵ log_a x = ( log_abx) / (log_aba)
∴ The given expression = [[(log_abx) / (log_aba)] / [( log_abx )] - ( log_ab)
= (1/log_aba) - log_ab = log_aab - log_ab = log_a(ab/b)
= log_aa = 1

Correct Option: B

∵ log_a x = ( log_abx) / (log_aba)
∴ The given expression = [[(log_abx) / (log_aba)] / [( log_abx )] - ( log_ab)
= (1/log_aba) - log_ab = log_aab - log_ab = log_a(ab/b)
= log_aa = 1

Given Exp.= log₂3 x log ₃2 x log₃4 x log₄3
= (log3 / log2) x ( log2 / log3) x (log4 / log3) x (log3 / log4)

Correct Option: A

Given Exp.= log₂3 x log ₃2 x log₃4 x log₄3
= (log3 / log2) x ( log2 / log3) x (log4 / log3) x (log3 / log4) = 1