Question

27²ⁿ⁻¹ = (243)³ में n का मान क्या होगा? 1️⃣ 3 2️⃣ 7 3️⃣ 9 4️⃣ 6​

Answer 1

Answer:

3

check by putting 3 in place on n

Answer 2

उतर :-

→ 27^(2n - 1) = (243)³

→ (3 * 3 * 3)^(2n - 1) = (3 * 3 * 3 * 3 * 3)³

→ (3³)^(2n - 1) = (3⁵)³

दोनों तरफ (a^m)^n = a^(m * n) का प्रयोग करने पर,

→ (3)^{3 * (2n - 1)} = 3^(5 * 3)

→ (3)^(6n - 3) = 3¹⁵

अब, यदि a^m = a^n हो तब, m = n होता है,

→ 6n - 3 = 15

→ 6n = 15 + 3

→ 6n = 18

→ n = 3 (Ans.)

देखते है n = 3 रख कर ,

→ 27^(2n - 1) = (243)³

→ 27^(2 * 3 - 1) = (243)³

→ 27^(6 - 1) = (243)³

→ (27)⁵ = (243)³

→ (3³)⁵ = (3⁵)³

→ 3¹⁵ = 3¹⁵

→ LHS = RHS

इसलिए , n का मान (1) 3 होगा ll

यह भी देखें :-

*यदि (-2)ⁿ⁺¹ × (-2)³ = (-2)⁷ है, तो k का मान ज्ञात कीजिए।* 1️⃣ k = 3 2️⃣ k = 4 3️⃣ k = 6 4️⃣ k = 8

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