Question

Решите логарифмическое уравнение на листочке​

Answer 1

log(a^k) b = 1/k * log(a) b

ОДЗ x>0

log(3) x + log(9) x + log(27) x = 11/12

log(3) x + log(3^2) x + log(3^3) x = 11/12

log(3) x + 1/2 *log(3) x + 1/3 *log(3) x = 11/12

11/6 * log(3) x = 11/12

log(3) x = 1/2

x = √3

Answer 2

Объяснение:

$log_3x+log_9x+log_{27}x=\frac{11}{12};log_3x+log_{3^2}x+log_{3^3}x=\frac{11}{12};\\log_3x+\frac{1}{2}log_3x+\frac{1}{3}log_3x=\frac{11}{12};t=log_3x;\\t+\frac{1}{2}t+\frac{1}{3}t=\frac{11}{12};t(1+\frac{1}{2}+\frac{1}{3})=\frac{11}{12};\\t*\frac{11}{6}=\frac{11}{12};t=\frac{11}{12}*\frac{6}{11}=\frac{1}{2};\\log_3x=\frac{1}{2};x=3^{\frac{1}{2}}=\sqrt{3}$