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Find the value of ‘x’ if (16)3x – 7 × (2)8x = (4)9x – 2 × (8)2 – x.

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Find the value of ‘x’ if (16)3x – 7 × (2)8x = (4)9x – 2 × (8)2 – x.
1). 2
2). 4
3). 6
4). 8


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Answered by on | Votes 2 |

Given,

⇒ (16)3x – 7 × (2)8x = (4)9x – 2 × (8)2 – x

⇒ (24)3x – 7 × (2)8x = (22)9x – 2 × (23)2 – x

⇒ (2)12x – 28 × (2)8x = (2)18x – 4 × (2)6 – 3x

⇒ (2)12x – 28 + 8x = (2)18x – 4 + 6 – 3x

⇒ (2)20x – 28 = (2)15x + 2

Equating powers of 2,

⇒ 20x – 28 = 15x + 2

⇒ 20x – 15x = 28 + 2

⇒ 5x = 30

∴ x = 30/5 = 6

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