Question

root of 6^n==1269 then what is n??

Answer 1

Value of n is 8

Correcting the question:

To find n, given √(6ⁿ) = 1296

Step-by-step explanation:

Given,

√(6ⁿ) = 1296

or, (6ⁿ)^(1/2) = 1296

Squaring both sides, we get

(6ⁿ)^(2/2) = (1296)²

or, 6ⁿ = (6⁴)²

or, 6ⁿ = 6⁸

Comparing the like powers of 6 from both sides, we get

n = 8

However this problem can be solved with another approach:

Given,

√(6ⁿ) = 1296

or, (6ⁿ)^(1/2) = 6⁴

or, 6^(n/2) = 6⁴

Comparing the like powers of 6 from both sides, we get

n/2 = 4

or, n = 8

Laws of indices:

• √a = a^(1/2)

• (aᵇ)ᶜ = aᵇᶜ

• If aᵇ = aᶜ, then b = c