Question

How do you evaluate $\log 1$?

Answer 1

Calculate the value of $\log 1$

The definition of logarithm function, ${\log }_{a}b=x$ can be written in the form of an exponential function as given below:

Then,$a^x=b$

To find the value of $\log 1$ since the base is not defined here, let us consider the base as $10$

Hence, we can write$\log 1$as ${\log }_{10}1$

Now, from the logarithm definition, we have the value of $a=10$ and $b=1$ Such that,

${\log }_{10}1=x$

By the logarithm rule, rewrite the above expression as

${10}^x=1$

Any number raised to the power $0$ is equal to $1$ . Thus,$10$ raised to the power $0$ makes the above expression true.

${10}^0=1$

This will be a condition for all the base values of $\log$, where the base raised to the power $0$ will give the answer as $1$

Hence the value of $\log 1$is $0$.