Question

Реши уравнение 2log3x+log3100−2=0
log3-в основании

Answer 1

$2 log_{3}x + log_{3}100 - 2 = 0 \\ log_{3} {x}^{2} + log_{3}100 - log_{3}9 = 0 \\ log_{3}( {x}^{2} \times 100 \div 9) = 0 \\ {3}^{0} = 100{x}^{2} \div 9 \\ 9 = 100x ^{2} \\ \frac{9}{100} = {x}^{2} \\ x = \sqrt{ \frac{9}{100} } = \frac{3}{10} = 0.3$