Question

How do you evaluate ${{\log }_{6}}6$ ?

Answer 1

Hint: In this question, we have to simplify a logarithm function. Thus, we will apply the logarithm formula to get the required solution. So, first we will use the logarithm formula ${{\log }_{b}}a=\dfrac{\log a}{\log b}$ in the equation. As we know, in the division, the same terms will cancel out and we get the remainder 0 and quotient 1, thus we will make the necessary calculations, to get the required answer for the problem.

Complete step-by-step solution:
According to the question, we have to simplify a logarithmic function.
So, to solve this problem, we will use the logarithm formula.
The function given to us is ${{\log }_{6}}6$ ---------- (1)
Now, we will apply the logarithm formula ${{\log }_{b}}a=\dfrac{\log a}{\log b}$ in equation (1), we get
$\Rightarrow {{\log }_{6}}(6)=\dfrac{\log 6}{\log 6}$
As we know, in the division, the same terms will cancel out and we get the remainder 0 and quotient 1, therefore we get
$\Rightarrow 1$
Therefore, for the function ${{\log }_{6}}6$, we get the value 1 , which is our required answer.

Note: While solving this problem, mention all the steps and formulas you are using while solving your problem. One of the alternative methods to solve this problem is converting the logarithm into the exponential function.
An alternative method:
The function: ${{\log }_{6}}6$
Let us first rewrite the above function as an equation, we get
${{\log }_{6}}(6)=x$ ---------- (1)
So, we will rewrite the equation (1) into an exponential equation because if ${{\log }_{a}}b=x$ then ${{a}^{x}}=b$ , therefore we get
$\Rightarrow {{6}^{x}}=6$
Since the bases are the same in the above equation, the two terms are equal if their powers will be equal, thus we get
$\Rightarrow x=1$ which is our required solution.