Question

Log3x+ log9x+ log27x=11

Answer 1

$log_3x+log_9x+log_{27}x=11; ; ; ; x textgreater 0\\log_3x+log_{3^2}x+log_{3^3}x=11\\log_3x+ frac{1}{2}log_3x+ frac{1}{3}log_3x=11\\(1+ frac{1}{2}+ frac{1}{3})log_3x=11\\ frac{11}{6}log_3x=11\\log_3x=11: frac{11}{6}\\log_3x=6\\x=3^6\\x=729$