Nilai 2log18-2log8√2+2log1/27-2log1/3

[tex]$\begin{align}&^2\log18-{^2}\log8\sqrt2+{^2}\log\frac1{27}-{^2}\log\frac13\\\\&={^2}\log\left(\frac{18}{8\sqrt2}\times\frac{\frac1{27}}{\frac13}\right)\\&={^2}\log\left(\frac9{4\sqrt2}\times\frac{\sqrt2}{\sqrt2}\times\frac3{27}\right)\\&={^2}\log\left(\frac{9\sqrt2}{4\cdot2}\times\frac19\right)\\&={^2}\log\left(\frac18\sqrt2\right)\\&={^2}\log\left(2^{-3}\times2^{\textstyle\frac12}\right)\\&={^2}\log2^{-\textstyle\frac52}\\&=\boxed{-\frac52}=\boxed{-2\frac12}\end[/tex]