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$\large 3^{\log_{3}^{2}x}+x^{\log_{3}x}=162$

=> $\large (3^{\log_{3}x})^{\log_{3}x}+x^{\log_{3}x}=162$

=>$\large (x)^{\log_{3}x}+x^{\log_{3}x}=162$                   [ $\large 3^{\log_{3}x}=x$]

=>$\large 2x^{\log_{3}x}=162$

=>$\large x^{\log_{3}x}=81$

taking log both the side with base 3,

=>$\large \log_{3}^{2}x=\log_{3}81$

=>$\large \log_{3}^{2}x=4$

=>$\large \log_{3}x=\pm 2$

so $\large x=9$ or $\large x=\frac{1}{9}$
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