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What should come at the place of ‘x’ in the following equation? 1252 × 57 ÷ 252 × 100 ÷ 8 = 125 × 8 × 58 ÷ 16x

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What should come at the place of ‘x’ in the following equation?

1252 × 57 ÷ 252 × 100 ÷ 8 = 125 × 8 × 58 ÷ 16x
1). 1/4
2). 1/2
3). 1
4). 1/5


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Answered by on | Votes 0 |

Given equation,

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

Taking into base factors,

⇒ 56 × 57 ÷ 54 × 52 × 22 ÷ 23 = 53 × 23 × 58 ÷ 24x

⇒ 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

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