Short answers, pulled from the story.
John Napier published the book titled Mirifici Logarithmorum Canonis Descriptio in 1614. This publication introduced a mathematical function that transformed complex multiplications and divisions into simple additions and subtractions for astronomers and navigators.
Henry Briggs compiled the first table of logarithms in 1617 using base 10. The table listed values for integers from 1 to 1000 with a precision of 14 digits and set the standard for all future computational tables.
The area under the curve y equals 1 over x corresponds to the logarithm of the x-coordinate. This geometric discovery was published by Grégoire de Saint-Vincent in 1647 and linked the logarithm to the constant e.
The strength of an earthquake is measured by taking the common logarithm of the energy emitted, known as the moment magnitude scale or the Richter magnitude scale. A 5.0 earthquake releases 32 times the energy of a 4.0, while a 6.0 releases 1000 times the energy of a 4.0.
The complex logarithm of a number z is given by the natural logarithm of r plus i times theta plus 2k pi i, where k is an arbitrary integer. This formula represents the natural logarithm of the absolute value r plus i times the argument theta.