Question

5 ^ log3x + x^log35 = 50

Answer 1

ОДЗ :  x < 0  ;  x ≠ 1

$5^{log_{3}x }+x^{log_{3}5 }=50\\\\5^{log_{3}x }=x^{log_{3}5} \ \Rightarrow \ x^{log_{3}5 }+x^{log_{3}5}=50\\\\2x^{log_{3}5}=50\\\\x^{log_{3}5}=25\\\\log_{3}x^{log_{3}5}=log_{3}25\\\\log_{3}5* log_{3}x=2log_{3}5\\\\log_{3}x=2\\\\\boxed{x=9}$