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

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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Description

Test your knowledge of natural logarithms and the mathematical constant e with this quiz. Explore the properties and applications of natural logarithms, and gain a deeper understanding of their significance in mathematics and science.