If 10 ^0.3010 = 2, then find the value of log _0.125 125.?

Correct Answer: 64

Explanation:

? log₂³ x¹ +log₂² x¹ + log₂x = 11
? 1/3log₂x + 1/2log₂x + log₂x = 11
? (1/3 + 1/2 +1)log₂x = 11
? 11/6log₂x = 11
? log₂x = 11 x 6 / 11 =6
? x = 2⁶ = 64

Correct Answer: 5

Explanation:

? 5^5-x = 2^x-5
? 5^5-x = 2^-(5-x)
? (5-x)log 5 = -(5-x)log 2
? (5-x)log 5 + (5-x)log 2 = 0
? (5-x){log 5 + log 2 } = 0
? (5-x){log10/2 + log 2 } = 0
? (5-x){log10 - log 2 + log 2} = 0
? 5-x = 0
? x = 5

Correct Answer: 0.159

Explanation:

? (1000)^x = 3
? xlog 10³ = log 3
? 3x = log 3
? x = log 3 / 3 = 0.477 / 3 = 0.159

Correct Answer: 2

Explanation:

? 2log₄x = 1 + log₄(x-1)
? log₄x² = log₄4 + log₄(x-1)
? x² = 4(x-1)
? x² - 4x + 4 = 0
? (x-2)² = 0
? x = 2

Correct Answer: 0.4771

Explanation:

Given log90 = 1.9542
? log(3² x 10) = 1.9542
? 2log 3 + log 10 = 1.9542
? log 3 = 0.9542 / 2 = 0.4771

Correct Answer: Can't be determined

Explanation:

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

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: 1

Explanation:

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

Correct Answer: - 1 / 2

Explanation:

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

Correct Answer: 15

Explanation:

Given Exp. = log₁₀10 + log₁₀100 + log₁₀1000 + log₁₀10000 + log₁₀100000
= 1 + 2 + 3 + 4 + 5
= 15