If log 3 = 0.477 and (1000) ^x = 3, then x equals to?

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: 0

Explanation:

Given expression = log x + log1/x
= log x + log 1 - log x
= log 1
= 0

Correct Answer: x2 + x - 1 = 0

Explanation:

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

Correct Answer: 0

Explanation:

Given expression = log 8 + log (1/8)
= log 8 x (1/8)
= log 1
= 0

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: 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: - 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: 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