Question

Find the value of 1/3 log 27- 2 log 1/3?​

Answer 1

Given,

$\[\frac{1}{3}\log 27 - 2\log \frac{1}{3}\]$

Solution,

$\[ = \frac{1}{3}\log 27 - 2\log \frac{1}{3}\]$

$\[ = \log {3^{\frac{3}{3}}} - \log {\left( {\frac{1}{3}} \right)^2}\]$

$\[ = \log 3 - \log \frac{1}{9}\]$

$\[ = \log 3 - \log {9^{ - 1}}\]$

$\[ = \log 3 + \log 9\]$

$\[ = \log \left( {3 \times 9} \right)\]$

$\[\begin{array}{l} = \log 27\\ = 3\log 3\end{array}\]$

Hence the value is $\[3\log 3\]$