Question

2raise to power x-1 × 5rise to power x-4 = 1250

Answer 1

Sol:
Given 2n-7 * 5n-4 = 1250

Here 1250 = 2 x 5 x 5 x 5 x 5 = 2 x 54

Now 2n-7 × 5n-4 × 23 = 2 × 54 × 23 [ multiply 23 on both sides ]

⇒ 2n - 7 + 3 × 5n-4 = 24 × 54

⇒ 2n - 4 × 5n-4 = 24 × 54

⇒ 10n - 4 = 104

bases are equal powers should be equated

⇒ n - 4 = 4

∴n = 8

Answer 2

Sol:
Given 2n-7 * 5n-4  = 1250

Here 1250 = 2 x 5 x 5 x 5 x 5 = 2 x 54

Now 2n-7 × 5n-4 × 23 = 2 × 54 × 23      [ multiply 23  on both sides ]

⇒ 2n - 7 + 3 × 5n-4  = 24 × 54

⇒ 2n - 4 × 5n-4  = 24 × 54

⇒ 10n - 4  = 104

bases are equal powers should be equated

⇒ n - 4 = 4

∴n = 8