Integration of loge x = In x = 2.303 log10 x

This text discusses the integration of the equation loge x = In x = 2.303 log10 x between the limits x = 0, when t = 0 and x = x, when t = t. The integration is performed using the following steps:

1. The equation is rewritten as a definite integral.
2. The integral is evaluated using the power rule of integration.
3. The result is simplified.

Here are some questions and answers about the integration:

• What is the equation that is being integrated?
• What are the limits of integration?
• What is the power rule of integration?
• What is the simplified result of the integration?

The answers to these questions are as follows:

• The equation that is being integrated is loge x = In x = 2.303 log10 x.
• The limits of integration are x = 0, when t = 0 and x = x, when t = t.
• The power rule of integration states that the integral of x^n is (x^(n + 1)) / (n + 1).
• The simplified result of the integration is a = 2.303 t.