Natural Logarithms and e Quiz

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Questions and Answers

What is the natural logarithm of 7.5?

  • $ln 7.5 = 0.6931$
  • $ln 7.5 = 1.3863$
  • $ln 7.5 = 3.1781$
  • $ln 7.5 = 2.0149$ (correct)

How is the natural logarithm of x generally written?

  • log$_{10}$ x
  • log$_e$ x
  • ln x (correct)
  • log x

What is the natural logarithm of e?

  • $ln e = 2$
  • $ln e = 0$
  • $ln e = 0.5$
  • $ln e = 1$ (correct)

What does the natural logarithm of 1 equal to?

<p>$ln 1 = 0$ (D)</p> Signup and view all the answers

How can the natural logarithm be defined for any positive real number a?

<p>As the area under the curve $y = 1/x$ from 1 to a (D)</p> Signup and view all the answers

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Study Notes

Natural Logarithm

  • The natural logarithm of 7.5 is approximately 2.01.
  • The natural logarithm of x is generally written as ln(x).
  • The natural logarithm of e is equal to 1, since e is the base of the natural logarithm.
  • The natural logarithm of 1 is equal to 0, since any number raised to the power of 0 is 1.
  • The natural logarithm can be defined for any positive real number a as the power to which the base e must be raised to produce a.

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