[tex]\dfrac{lg(3^3)-lg3+lg2}{lg(2\cdot 3)}=\dfrac{lg(3^3)-lg3+lg2}{lg(2\cdot 3)}=\dfrac{lg\left(\dfrac{3^3}{3}\right)+lg2}{lg(2\cdot 3)}=\\\\=\drac{lg(3^2)+lg2}{lg6}=\dfrac{lg(9\cdot2)}{lg6}=\dfrac{lg18}{lg6}=\dfrac{lg(6\cdot 3}{lg6}=\\\\=\dfrac{lg6+lg3}{lg6}=1+\dfrac{lg3}{lg6}=1+log_36.[/tex]
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