If (√3)⁵ × 9² = 3ⁿ × 3√3, then what is the value of n?
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Correct answer: C
Explanation
Given:
(√3)⁵ × 9² = 3ⁿ × 3√3
By the formula:
√3 = 3¹ᐟ²
9 = 3²
(√3)⁵ = (3¹ᐟ²)⁵ = 3⁵ᐟ²
9² = (3²)² = 3⁴
3⁵ᐟ² × 3⁴
= 3(5/2 + 4)
= 3(5/2 + 8/2)
= 3¹³ᐟ²
3ⁿ × 3√3
= 3ⁿ × 3 × 3¹ᐟ²
= 3ⁿ × 3³ᐟ²
= 3(n + 3/2)
3¹³ᐟ² = 3(n + 3/2)
13/2 = n + 3/2
n = 5