3log3x2 + xlog3x = 162Let log3x = m⇒x = 3mNow, the above equation becomes : 3m2 + 3mm = 162⇒3m2 + 3m2 = 162⇒2×3m2 = 162⇒3m2 = 1622⇒3m2 = 81⇒3m2 = 34⇒m2 = 4⇒m = 2So, x = 3m = 32 = 9

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3^{{(\log_{3} x)}^{2}} + x^{\log_{3} x} = 162 Let \log_{3} x = m \Rightarrow x = 3^{m} Now, the above equation becomes : 3^{m^{2}} + {(3^{m})}^{m} = 162 \Rightarrow 3^{m^{2}} + 3^{m^{2}} = 162 \Rightarrow 2 \times 3^{m^{2}} = 162 \Rightarrow 3^{m^{2}} = \frac{162}{2} \Rightarrow 3^{m^{2}} = 81 \Rightarrow 3^{m^{2}} = 3^{4} \Rightarrow m^{2} = 4 \Rightarrow m = 2 So, x = 3^{m} = 3^{2} = 9

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