<img src="https://tex.z-dn.net/?f=%7Bx%7D%5E%7B%20log_%7B3%7D%28x%29%20%7D%20%20%3D%2081%20%7Bx%7D%5E%7B3%7D%20" id="TexFormula1

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3 years ago

" 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?

Mathematics

1 answer:

BlackZzzverrR [31]3 years ago

3 0

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$

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