Find x: if [9/5]⁻⁵ × [9/5]¹² = [9/5]^3x−2

The correct answer is: Value of x for the given equation is 3.

Step-by-step solution:-
[9/5]⁻⁵ × [9/5]¹² = [9/5]^3x−2
∴ [5/9]⁵ × [9/5]¹² = [9/5]^3x−2 ................................. (b^-n = 1 / bⁿ)
∴ 5⁵ / 9⁵ × 9¹² / 5¹² = [9/5]^3x-2 ................................. [aⁿ / bⁿ = (a/b)ⁿ]
∴ 5^5× 9¹² / 9⁵ × 5¹² = [9/5]^3x-2
∴ 9^12-5 / 5^12-5 = [9/5]^3x-2 ................ (aⁿ / a^m = a^n-m)
∴ 9⁷ / 5⁷ = [9/5]^3x-2
∴ [9/5]⁷ = [9/5]^3x-2 ................................. [aⁿ / bⁿ = (a/b)ⁿ]
∴ 7 = 3x-2 ................................. (Exponents of the same base in an equation are equal)
∴ 7 + 2 = 3x
∴ 9 = 3x
∴ 9/3 = x
∴ 3 = x
i.e. x = 3
Final Answer:-
∴ Value of x for the given equation is 3.