(36√6 + 6^5/2 / 108×12)^2=6^n , then find the value of n? (\frac{36√(6)+6^{(5)/(2)}}{108*12})^(2)=6^(n) \\ Thank you.....​

Question

(36√6 + 6^5/2 / 108×12)^2=6^n , then find the value of n?


`(\frac{36√(6)+6^{(5)/(2)}}{108*12})^(2)=6^(n) \\`


Thank you.....​

Answer 1

Explanation:

Given: [{36√(6) + 6^(5/2)} / (108×12)]² = 6ⁿ

Asked: Find the value of n = ?

EXPLANATION:

Given that:

[{36√(6) + 6^(5/2)} / (108×12)]² = 6ⁿ

⇛[{(6)² * (6)^(1/2) * (6)^(5/2}/(36 * 3 * 12)]² = 6ⁿ

⇛[{6² * 6^(1/2) * 6^(5/2)}/(36 * 36)]² = 6ⁿ

⇛[{6² * 6^(1/2) * 6^(5/2)}/(6*6 * 6*6)]² = 6ⁿ

⇛[{6² * 6^(1/2) * 6^(5/2)}/(6² * 6²)]² = 6ⁿ

⇛(6³⁻²)² = 6ⁿ

⇛(6¹)² = 6ⁿ

⇛6² = 6ⁿ

When an exponential has the same base on each side, then the exponents must be equal.

Therefore, n = 2.

Answer: The Value of “n” for the given problem is 2.