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Question: What is \[\ln \] of \[0.100\\# \]?...

What is ln⁡\ln of 0.100\\# ?

Explanation

Solution

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=10−10.100 = {10^{ - 1}}
Hence log⁡ 0.100=−1\log \,0.100 = - 1
As ln⁡ 0.100=log⁡ 0.100log⁡ e −\ln \,0.100 = \dfrac{{\log \,0.100}}{{\log \,e}}\, - here log is used with base 1010.
Now we can find,
ln⁡ 0.100 =−1log⁡ e=−10.4343=−2.3026\ln \,0.100\, = - \dfrac{1}{{\log \,e}} = - \dfrac{1}{{0.4343}} = - 2.3026
Therefore ln⁡\ln of0.1000.100is −2.3026 - 2.3026
Thus we found the final answer for the question as −2.3026 - 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{\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.