Question

How do you evaluate \[{\log _3}1\]?

Answer 1

Hint: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.