Exp. = log_0.125125 = log₂^-3 5³ = - 3/3log₂5 = -log₂5
∵ 10^0.3010 = 2
⇒ log₁₀2 = 0.3010
∵ log₁₀5 = log₁₀10/2 = log₁₀10-log₁₀2
= 1-0.3010 = 0.6990

Correct Option: B

Exp. = log_0.125125 = log₂^-3 5³ = - 3/3log₂5 = -log₂5
∵ 10^0.3010 = 2
⇒ log₁₀2 = 0.3010
∵ log₁₀5 = log₁₀10/2 = log₁₀10-log₁₀2
= 1-0.3010 = 0.6990
∴ -log₂5 = - log₁₀⁵ / log₁₀²
= - 0.6990 / 0.3010 = - 699/301

Exp. = log_0.12564 = log₂^-3 2⁶
={6 / (-3)} log₂2

Correct Option: D

Exp. = log_0.12564 = log₂^-3 2⁶
={6 / (-3)} log₂2
= -2

Exp. =log₃₂2⁸ + log₂₄₃3⁷ - log₃₆1296
= log₂⁵ 2⁸ + log₃⁵ 3⁷ - log₃₆ 36²
= (8/5)log₂2 + (7/5)log₃3 - 2log₃₆36

Correct Option: C

Exp. =log₃₂2⁸ + log₂₄₃3⁷ - log₃₆1296
= log₂⁵ 2⁸ + log₃⁵ 3⁷ - log₃₆ 36²
= (8/5)log₂2 + (7/5)log₃3 - 2log₃₆36
= 8/5 + 7/5 - 2 = 1

Exp. = log₄₉16807 - log₉27
= log₇² 7⁵ - log₃² 3³
=(5/2)log₇7 - (3/2)log₃3

Correct Option: B

Exp. = log₄₉16807 - log₉27
= log₇² 7⁵ - log₃² 3³
=(5/2)log₇7 - (3/2)log₃3
=5/2 - 3/2
= 1