Question

How do you evaluate \[{{\log }_{3}}3\]?

Answer 1

Hint: The \[\log \] with input value as \[a\] and the base value as \[b\] then according to the property of logarithm this is equal to the \[\log \] with some base \[t\] and input value as \[a\] divided by the \[\log \]with same base \[t\] and input value as \[b\].
\[\Rightarrow {{\log }_{b}}a=\dfrac{{{\log }_{t}}a}{{{\log }_{t}}b}\].

Complete step by step solution:
To evaluate the given value \[{{\log }_{3}}3\] we will use the property of logarithm that is
\[\Rightarrow {{\log }_{b}}a=\dfrac{{{\log }_{t}}a}{{{\log }_{t}}b}\]
Now comparing this with given question
\[a=3\] and \[b=3\]
\[\Rightarrow {{\log }_{3}}3=\dfrac{{{\log }_{t}}3}{{{\log }_{t}}3}\]
Since the above numerator and denominator are equal that gives value \[1\]
\[\Rightarrow {{\log }_{3}}3=\dfrac{{{\log }_{t}}3}{{{\log }_{t}}3}=1\]

Hence the value after evaluation is equal to \[1\].

Note: First of all recall all the properties of logarithm and then identify which property is applicable in a particular question. We have another user that is also derived from the above property that the value of logarithm with the same base and same input value equals unity that is \[1\].