log ₁₀10 + log ₁₀100 + log ₁₀1000 + log ₁₀10000 + log ₁₀100000 is equal to?

Correct Answer: - 1 / 2

Explanation:

log₉ 81 - log₄ 32 = log₃² 3⁴ - log₂² 2⁵
= 4/2 - 5/2 = -1/2

Correct Answer: 1

Explanation:

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

Correct Answer: 1

Explanation:

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

Correct Answer: Can't be determined

Explanation:

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

Correct Answer: - 699 / 301

Explanation:

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

Correct Answer: None of these

Explanation:

log₁₀xy = z
? xy = 10^z
? x = 10^z/y

Correct Answer: 4

Explanation:

Let log_-1/381 = x
? 81 = (-1/3)^x
? 3⁴ = (-1/3)^x = 3^-x
? x = -4

Correct Answer: 101010

Explanation:

If log₁₀{log₁₀[log₁₀(log₁₀N)]} = 0
? log₁₀{log₁₀(log₁₀N)} = 1
? log₁₀(log₁₀N) = 10
? log₁₀^N = 10¹⁰
? N = 10¹⁰¹⁰

Correct Answer: 16

Explanation:

Exp. = 25 log₅4 = 5² log₅4
= 5 log₅ 4²
= 16

Correct Answer: - 6

Explanation:

Exp. = log₁₀ 10^-6 = -6