Question

How do you evaluate $\log 1$?

Answer 1

Hint: Generally, for finding the log of a given number, it is advised to break the log of a number to the form for which you can predict its value using the logarithmic functions. Logarithmic function is defined as the inverse of exponentiation and is given by, $F(x) = {\log _a}x$, where the most commonly used logarithmic functions are base 10.

Complete step-by-step answer:
According to the given question, we need to evaluate $\log 1$, where the logarithmic function is base 10.
So, $\log 1$ can be written as: ${\log _{10}}1$
Considering, ${\log _{10}}1$
Writing it in other form, ${10^{{{\log }_{10}}1}} = {10^x}$
Also, it should be noted that $10$ raised to a log base $10$ of something is that something.
${10^x} = 1$

We only get $1$ as a result when Anything is raised to $0$.

Hence, we get $x = 0$

Thus, ${\log _{10}}1 = 0$.

Therefore, $\log 1$ is equivalent to $0$.

Note: We have to be very careful about the domain in which the logarithmic function is defined. For example in this case, the log base is $10$. Logarithmic function is defined for all values of log base except for $1$ and negative values. If it would have asked us to evaluate ${\log _1}1$, and we would have proceeded in the same way, then certainly the answer obtained would have been wrong because ${\log _1}1$is an undefined function.