ডেইলি কুইজ [২০০ দিন]

(³√3 × √2)⁶
= (3^1/3 × 2^1/2)⁶
= 3² × 2³
= 9 × 8
= 72

2^x + 2^x + 2^x + 2^x = 1
বা, 4.2^x = 1
বা, 2².2^x = 2°
বা, 2^{x + 2} = 2⁰
বা, x + 2 = 0
∴ x = -2

(125)^{(2x - 3)/3} = (1/5)^{3x - 6}
বা, (5³)^{(2x - 3)/3} = (5^-1)^{3x - 6}
বা, 5^{2x - 3} = 5^{-3x + 6}
বা, 2x - 3 = -3x + 6
বা, 5x = 9
∴ x = 9/5

8^5/3 ÷ 8^2/3
= 8^5/3/8^2/3
= 8^{(5/3) - (2/3)}
= 8^3/3
= 8¹
= 8

(125/27)^-(2/3)
= (5³/3³)^-(2/3)
= {(5/3)³}^-(2/3)
= (5/3)^-2
= (3/5)²
= 9/25

(2^{x + 4} - 4.2^{x + 1})/2^{x + 2}
= (2^x.2⁴ - 2².2^x.2)/2^x.2²
= (16.2^x - 8.2^x)/4.2^x
= (16 - 8)/4
= 8/4
= 2

m^-3 = 0.5 = 1/2
বা, 1/m³ = 1/2
বা, m³ = 2
বা, (m³)² = 2²
∴ m⁶ = 4

(2n)ⁿ = n²ⁿ
বা, 2ⁿ.nⁿ = n²ⁿ
বা, 2ⁿ = n^{2n - n}
বা, 2ⁿ = nⁿ
বা, n = 2
∴ m = 4

{(4^{m + 1})/((2^{m - 1})^{m + 1})} ÷ {(2^{m + 1})/(2^{m2 - m}}
= {((2²)^{m + 1})/(2^{m2 - 1}} ÷ {(2^{m + 1})/2^{m2 - m}}
= (2^{2m + 2}/2^{m2 - 1}) × (2^{m2 - m}/2^{m + 1})
= (2^{2m + 2 + m2 - m})/(2^{m2 - 1 + m + 1)}
= (2^{m2 + m + 2})/(2^{m2 + m})
= 2^{m2 + m + 2 - m2 - m}
= 2²
= 4

log_a1/8 = -3
বা, a^-3 = 1/8
বা, a^-3 = 2^-3
∴ a = 2

log₅(0.04)
= log₅(1/25)
= log₅5^-2
= -2 log ₅5
= -2.1
= -2

log_(3√2)324 = x
বা, x = log_(3√2)(3√2)⁴ = 4 log_(3√2)3√2
= 4.1
= 4

log₂1024
= log₂2¹⁰
= 10 log₂2
= 10.1
= 10

log_x¹²⁵ = 3
বা, x³ = 125 = 5³
∴ x = 5