Question

What is \[\ln \] of \[0.100\# \]?

Answer 1

Hint: In 1614, John Napier, a Scottish mathematician, announced his discovery of logarithms. His job was to aid in the multiplication of quantities known as sines at the time. The value of the side of a right-angled triangle with a broad hypotenuse was the whole sine.

Complete step-by-step solution:
So after evaluating the question, we identified or understood that Napier's or natural logarithm, i.e. to base 10, is represented by ln. ln is called a natural algorithm. It is also called the logarithm of the base e.
Now we can represent \[0.100 = {10^{ - 1}}\]
Hence \[\log \,0.100 = - 1\]
As \[\ln \,0.100 = \dfrac{{\log \,0.100}}{{\log \,e}}\, - \] here log is used with base \[10\].
Now we can find,
\[\ln \,0.100\, = - \dfrac{1}{{\log \,e}} = - \dfrac{1}{{0.4343}} = - 2.3026\]
Therefore \[\ln \] of\[0.100\]is \[ - 2.3026\]
Thus we found the final answer for the question as \[ - 2.3026\]
Additional information:
The logarithm is the inverse function of exponentiation in mathematics. To put it another way, a logarithm is a power to which a number must be increased in order to obtain another number. It's also known as the base-10 logarithm or the common logarithm. A logarithm's general form is as follows:
\[{\log _a}(y) = x\]

Note: A logarithm is the number that must be raised to a certain power in order to get another number. The difference between log and ln is that log refers to base 10 while ln refers to base e. A natural logarithm is the power to which the base ‘e' must be increased in order to obtain a number known as its log number. The exponential function is denoted by the letter e.