If 3^(x+1) = 5^(x-2), then find the value of x. (Take log 5 = 0.6989 and log 3…

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If 3^(x+1) = 5^(x-2), then find the value of x.
(Take log 5 = 0.6989 and log 3 = 0.4771)

  1. A.

    5

  2. B.

    7.5

  3. C.

    11

  4. D.

    8.5

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Correct answer: D

Solution: Solve the equation 3^(x+1) = 5^(x-2) by taking logarithms.

  • Take logarithm of both sides: (x + 1) log 3 = (x - 2) log 5.

  • Expand: x log 3 + log 3 = x log 5 - 2 log 5.

  • Collect x terms: x (log 3 - log 5) = -2 log 5 - log 3.

  • Solve for x: x = (2 log 5 + log 3) / (log 5 - log 3).

  • Substitute the given values: numerator = 2 × 0.6989 + 0.4771 = 1.8749; denominator = 0.6989 - 0.4771 = 0.2218.

  • Compute: x = 1.8749 / 0.2218 ≈ 8.45, which rounds to 8.5.

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