Question

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

Answer 1

Answer:

n = 8

Step-by-step 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

Answer 2

Answer:

n = 8

Step-by-step 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