- #1

Jules18

- 102

- 0

## Homework Statement

True or false?

ln(1/10) = -[tex]\int[/tex] dx/x

## The Attempt at a Solution

I have no idea where to start on this one.

what is dx/x ??

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- Thread starter Jules18
- Start date

In summary, the natural logarithm function, denoted as ln(x) or log<sub>e</sub>(x), is the logarithm with base e and is the inverse function of the exponential function. It is closely related to the negative integral and has many important applications in mathematics and science. It is unique in its use of the constant e as its base and can be evaluated for negative or complex numbers, but is not defined for x ≤ 0.

- #1

Jules18

- 102

- 0

True or false?

ln(1/10) = -[tex]\int[/tex] dx/x

I have no idea where to start on this one.

what is dx/x ??

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- #2

jakncoke

- 16

- 0

-Integrate[1/x] with respect to x

- #3

Mark44

Mentor

- 37,745

- 10,089

I.e., does the integral look like this?

[tex]-\int_1^{10} \frac{dx}{x}[/tex]

- #4

Jules18

- 102

- 0

The natural logarithm function, denoted as ln(x) or log_{e}(x), is the logarithm with base e, where e is the mathematical constant approximately equal to 2.71828. It is the inverse function of the exponential function, meaning that if y = e^{x}, then x = ln(y).

The natural logarithm function and the negative integral are closely related because the natural logarithm of a number can be expressed as the negative integral of its reciprocal. In other words, ln(x) = −∫1/x dx. This relationship is known as the fundamental theorem of calculus.

The natural logarithm function has many important applications in mathematics and science. It is used to solve exponential equations, and it plays a crucial role in calculus, particularly in the study of continuous growth and decay. It is also used in statistics, physics, and engineering to model natural processes and phenomena.

The natural logarithm function is unique because it uses the constant e as its base, whereas other logarithmic functions use different bases. The natural logarithm function also has specific properties and applications that distinguish it from other logarithmic functions.

Yes, the natural logarithm function can be evaluated for negative or complex numbers. However, the result will be a complex number, and it is usually expressed in terms of its real and imaginary parts. Additionally, the natural logarithm function is not defined for x ≤ 0, as the logarithm of a non-positive number is undefined in the real number system.

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