Question

x^㏒₃X=81
............................

Answer 1

x > 0

$x^{log_{3}x }=81\\\\log_{3}x^{log_{3}x }=log_{3}81\\\\log_{3} x*log_{3}x=log_{3}3^{4}\\\\log^{2}_{3}x=4\\\\1)log_{3}x=2\\\\x_{1}=3^{2}=9\\\\2)log_{3}x=-2\\\\x_{2}=3^{-2}=\frac{1}{9}\\\\OTVET:\frac{1}{9};9$

Answer 2

Ответ:

Объяснение:

$x^{log_3(x)}=81;x>0\\log_x(x^{log_3(x)})=log_x(81)\\log_3(x)=log_x(81)\\log_3(x)=\frac{log_3(81)}{log_3(x)} \\log_3^2(x)=4\\log_3(x)=-2=>x=\frac{1}{9}\\log_3(x)=2=>x=9$