Question

What is the value of n when (9)^2n-1 =(27)^n+2

Answer 1

n = 8

Explanation:

9²ⁿ⁻¹ = 27ⁿ⁺²

(3²)²ⁿ⁻¹ = (3³)ⁿ⁺²

3⁴ⁿ⁻² = 3³ⁿ⁺⁶

4n - 2 = 3n + 6

4n - 3n = 6 + 2

n = 8

Answer 2

n = 8

Explanation:

Using the rule of exponents

`(a^m)^(n)` =
`a^(mn)`

Given

`(9)^(2n-1)` =
`(27)^(n+2)`, then

`(3^2)^(2n-1)` =
`(3^3)^(n+2)`

`3^(4n-2)` =
`3^(3n+6)`

Since the bases on both sides are equal, both 3 then equate the exponents

4n - 2 = 3n + 6 ( subtract 3n from both sides )

n - 2 = 6 ( add 2 to both sides )

n = 8