1252 × 57 ÷ 252 × 100 ÷ 8 = 125 × 8 × 58 ÷ 16x1). 1/42). 1/23).

1.	1252 × 57 ÷ 252 × 100 ÷ 8 = 125 × 8 × 58 ÷ 16x1). 1/42). 1/23). 14). 1/5
Answer» Given equation, ⇒ 125² × 5⁷ ÷ 25² × 100 ÷ 8 = 125 × 8 × 5⁸ ÷ 16^x Taking into base FACTORS, ⇒ 5⁶× 5⁷ ÷ 5⁴ × 5² × 2² ÷ 2³ = 5³× 2³ × 5⁸ ÷ 2^4x ⇒ 5^{(6 + 7 – 4 + 2)} × 2^{(2 – 3)} = 5^{(8 + 3)} × 2^{(3 – 4x)} ⇒ 5¹¹ × 2^-1 = 5¹¹ × 2^{(3 – 4x)} ⇒ 5^{(11 – 11)} = 2^{(3 – 4x + 1)} ⇒ 5⁰ = 2^{(4 – 4x)} ⇒ 1 = 2^{(4 – 4x)} ⇒ 2⁰ = 2^{(4 – 4x)} Equating powers, ⇒ 4 – 4x = 0 ⇒ x = 1

1252 × 57 ÷ 252 × 100 ÷ 8 = 125 × 8 × 58 ÷ 16x1). 1/42). 1/23). 14). 1/5

Answer»

Given equation,

⇒ 125² × 5⁷ ÷ 25² × 100 ÷ 8 = 125 × 8 × 5⁸ ÷ 16^x

Taking into base FACTORS,

⇒ 5⁶× 5⁷ ÷ 5⁴ × 5² × 2² ÷ 2³ = 5³× 2³ × 5⁸ ÷ 2^4x

⇒ 5^{(6 + 7 – 4 + 2)} × 2^{(2 – 3)} = 5^{(8 + 3)} × 2^{(3 – 4x)}

⇒ 5¹¹ × 2^-1 = 5¹¹ × 2^{(3 – 4x)}

⇒ 5^{(11 – 11)} = 2^{(3 – 4x + 1)}

⇒ 5⁰ = 2^{(4 – 4x)}

⇒ 1 = 2^{(4 – 4x)}

⇒ 2⁰ = 2^{(4 – 4x)}

Equating powers,

⇒ 4 – 4x = 0

⇒ x = 1