Question

" title="{x}^{ log_{3}(x) } = 81 {x}^{3} " alt="{x}^{ log_{3}(x) } = 81 {x}^{3} " align="absmiddle" class="latex-formula">
can you solve by algebraically, not graphing and provide step by step explanation, please?​

Answer 1

Answer:

x=81 or 1/3

Step-by-step 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$