If _ x (2x-1)¹⁹ (3x+2)¹¹ (6x-5)³⁰ = 2^a 3^b , then a + b =

Step-by-step solution

_ x (2x-1)¹⁹ (3x+2)¹¹ (6x-5)³⁰ Dividing the numerator and the denominator by x³⁰ : _ x (2 - 1 x )¹⁹ (3 + 2 x )¹¹ (6 - 5 x )³⁰ As x , 1 x 0 . The limit evaluates to: 2¹⁹ 3¹¹ 6³⁰ Substituting 6 = 2 3 : 2¹⁹ 3¹¹ 2³⁰ 3³⁰ = 2^ 19 - 30 3^ 11 - 30 = 2⁻¹¹ 3⁻¹⁹ Comparing with 2^a 3^b , we get a = -11 and b = -19 . Therefore, a + b = -11 - 19 = -30 . Answer: -30