Question

What is the value of log6 1/36?

Answer 1

The value of ${\log _6}\left( {\dfrac{1}{{36}}} \right)$ is $\boxed{{{\log }_6}\left( {\frac{1}{{36}}} \right) = - 2}.$

Further explanation:

The logarithm properties can be expressed as follows,

(a). ${\log _a}a = 1$

(b). ${\log _a}{a^b} = b$

(c). ${\log _a}b = \dfrac{{\log b}}{{\log a}}$

Given:

The expression is ${\log _6}\left( {\dfrac{1}{{36}}} \right).$

Explanation:

The given expression is ${\log _6}\left( {\dfrac{1}{{36}}} \right).$

Consider the expression as A.

$\begin{aligned}{\text{A}} &= {\log _6}\left( {\frac{1}{{36}}} \right)\\&= {\log _6}\left( {\frac{1}{{{6^2}}}} \right)\\&= {\log _6}\left( {{6^{ - 2}}} \right)\\&= - 2\\\end{aligned}$

The value of ${\log _6}\left( {\dfrac{1}{{36}}} \right)$ is $\boxed{{{\log }_6}\left( {\frac{1}{{36}}} \right) = - 2}.$

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Number system

Keywords: place value, base value, decimal expansion, value, log value, log6, 1/36.

Answer 2

Answer:  The required value of the given expression is - 2.

Step-by-step explanation:  We are given to find the value of the following logarithmic expression:

$E=\log_6\dfrac{1}{36}.$

We will be using the following logarithmic properties:

$(i)~\log_ab=\dfrac{\log b}{\log a},\\\\(ii)\log a^b=b\log a.$

We have

$E\\\\=\log_6\dfrac{1}{36}\\\\\\=\log_6\dfrac{1}{6^2}\\\\\\=\log_66^{-2}\\\\\\=\dfrac{\log6^{-2}}{\log 6}\\\\\\=\dfrac{-2\log6}{\log6}\\\\\\=-2.$

Thus, the required value of the given expression is - 2.