{x}^{ log_(3)(x) } = 81 {x}^(3) can you solve by algebraically, not graphing and provide step by step explanation, please?​

Question

`{x}^{ log_(3)(x) } = 81 {x}^(3)`

can you solve by algebraically, not graphing and provide step by step explanation, please?​

Answer 1

x=81 or 1/3

Explanation:

`x^\log_3(x)} =81x^3\\\log_3(x^(\log_3(x)))=\log_3(81x^3)\\\(\log_3x)(\log_3x)=\log_381+\log_3x^3\\(\log_3x)^2=3\log_3x^+4\\\\Let u=\log_3x\\\\u^2-3u-4=0\\(u-4)(u+1)=0\\u=4 \\4=\log_3x\\x=3^4=81\\\\u=-1\\-1=\log_3x\\x=3^(-1)=1/3`