Question

log(3)x+log(9)x+log(81)x=7/4

Answer 1

ОДЗ
х>0

$log_3x+log_9x+log_{81}x= frac{7}{4} \\log_3x+log_3sqrt{x}+log_{3}sqrt[4]{x}= frac{7}{4}\\log_3(xcdot sqrt{x}cdot sqrt[4]{x})= frac{7}{4} \\ log_3(x^{ frac{7}{4} })= frac{7}{4}\\ frac{7}{4}log_3x= frac{7}{4} \\log_3x=1\\x=3$