10
advanced-math

If ln(x)=2\ln(x) = 2, what is xx?

A

e27.39e^2 \approx 7.39

B

22

C

1e2\frac{1}{e^2}

D

e2.718e \approx 2.718

Correct Answer: A

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

  1. Definition: ln(x)=y\ln(x) = y means ey=xe^y = x.
  2. Apply: ln(x)=2\ln(x) = 2 means x=e2x = e^2.
  3. Calculate: e27.389e^2 \approx 7.389.

💡 Strategic Tip:ln\ln and exe^x are inverse functions: eln(x)=xe^{\ln(x)} = x and ln(ex)=x\ln(e^x) = x.

Choice B is incorrect because this confuses the input and output. Choice C is incorrect because this inverts incorrectly. Choice D is incorrect because this is e1e^1, not e2e^2.