Question

3 log(4)^2 - 1/2 log (3)^9

Answer 1

Question:

$\\\tt 3log4^{2} - \dfrac{1}{2} log 3^{9}$

Answer:

$\\\tt log\dfrac{2^{12} }{3^{\frac{9}{2} } }$

Properties used:

$\\\tt log\ x^{y} = y\ log x\\\\log x - log y = log \dfrac{x}{y}$

Steps:

$\\\tt 3log4^{2} - \dfrac{1}{2} log 3^{9} \\ \\\tt = log 2^{12} - log3^{\frac{9}{2} } \\\tt = log\dfrac{2^{12} }{3^{\frac{9}{2} } }$