$ log _3 \frac{3+3\sqrt{\sqrt{27}}}{\sqrt{3}+5\sqrt{\sqrt{3}}+6}$
$ log _3 \frac{3+3(3^{\frac{3}{4}})}{(3^{\frac{1}{4} })^2+5(3^{\frac{1}{4} })+6}$
$ log _3 \frac{3(1+3^{\frac{3}{4}})}{(3^{\frac{1}{4} }+3) (3^{\frac{1}{4} }+2)}$
$ log _3 \frac{3(1+3^{\frac{3}{4}})}{ 3^{\frac{1}{4} }(1+3^{\frac{3}{4}}) (3^{\frac{1}{4} }+2)}$
$ log _3 \frac{3}{ 3^{\frac{1}{4} }(3^{\frac{1}{4} }+2)}$
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