Answers

1. Given the:

   ln(x + 6) – ln(2x – 1) = 1

   Using the logarithm rule:

   • ln a – ln b = ln (a/b)

   • ln((x + 6) / (2x – 1)) = 1
   • ((x + 6) / (2x – 1)) = E ¹

   We know,

   • e1 = ²’⁷²

   • ((x + 6) / (2x – 1)) ≈ 2.72

   Simplifying we get,

   • (x + 6) = 2.72 (2x – 1)

   • x + 6 = 2.72 (2x) – 2.72 (1)

   • x + 6 = 5.44x – 2.72

   • 8.72 = 4.44x

   By cross multiplication we get,

   • x = 8.72 / 4.44

   • x = 1.97

   Therefore, the value of x is 1.97.

   The correct option in the exercise ln (x + 6) – ln (2x – 1) = 1 is alternative “D”.

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