Answer:
[tex]\ln (\dfrac{(x^2-6)^{\frac{1}{3}}}{(3x+2)^2})[/tex]
Step-by-step explanation:
The given expression is
[tex]\dfrac{1}{3}\ln (x^2-6)-2\ln (3x+2)[/tex]
We need to rewrite the expression as the logarithm of a single quantity.
Using the properties of logarithm we get
[tex]\ln (x^2-6)^{\frac{1}{3}}-\ln (3x+2)^2[/tex] [tex][\because \log a^b = b\log a][/tex]
[tex]\ln (\dfrac{(x^2-6)^{\frac{1}{3}}}{(3x+2)^2})[/tex] [tex][\because \log a-log b = \log (\frac{a}{b})][/tex]
Therefore, the simplified form of the given expression is [tex]\ln (\dfrac{(x^2-6)^{\frac{1}{3}}}{(3x+2)^2})[/tex].
