8
advanced-math

Solve: ln⁡(x−2)=3\ln(x-2) = 3

A

x=e3+2≈22.09x = e^3 + 2 \approx 22.09

B

x=5x = 5

C

x=e3−2≈18.09x = e^3 - 2 \approx 18.09

D

x=3x = 3

Correct Answer: A

Choice A is the correct answer. Use the definition of natural logarithm.

  1. Given: ln⁡(x−2)=3\ln(x-2) = 3.
  2. Convert: x−2=e3x - 2 = e^3.
  3. Solve: x=e3+2≈20.09+2=22.09x = e^3 + 2 \approx 20.09 + 2 = 22.09.

💡 Strategic Tip:ln⁡(a)=b\ln(a) = b means a=eba = e^b.

Choice B is incorrect becauseln⁡(3)eq3\ln(3) eq 3. Choice C is incorrect because we add 2, not subtract. Choice D is incorrect becauseln⁡(1)=0eq3\ln(1) = 0 eq 3.

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