Question

How do you evaluate ${\log _3}1$?

Answer 1

As we all know that the function used in this question is a logarithmic function and it has certain properties. So in this question, we will use one of its properties that is ${\log _a}b = x$.
Then we can write it as $b = {a^x}$ and then by comparing both sides we can get values of x but before using this property we satisfy its conditions which make it defined in its domain.

Complete step by step solution:
We will use one of the logarithmic properties that is ${\log _a}b = x$
$\Rightarrow b = {a^x}$
Now, according to question ${\log _3}1 = x$ (say)
Now, we will have to find x
By applying logarithmic properties, we get
$1 = {3^x}$

As we can see that $1 = {3^x}$this equation will satisfy only in one condition that is x=0. So to satisfy this equation x needs to be 0. So the answer of ${\log _3}1 = 3$.

Note: While using this function we need to take care that base value must be greater than 0 and must not be equal to 1 that is ${\log _a}b,{\rm{ }}a > 0{\rm{ }}\& {\rm{ }}a \ne 1$.In this case, the log form and index form are interchangeable. we also have to take care that b also should be greater than zero. If these conditions are satisfied then only we will be able to solve the logarithmic function.