Question

Найдите нули функции y=log (2x-3)
²

Answer 1

$y=log_{a}(2x-3)^2\ \ ,\ \ \ \ ODZ:\ (2x-3)^2>0\ \ \to \ \ \ x\ne 1,5\\\\\\y=0\ \ \ \to \ \ \ log_{a}(2x-3)^2=0\ \ \ \to \ \ \ (2x-3)^2=1\ \ ,\\\\(2x-3)^2-1=0\ \ ,\ \ \ (2x-3-1)(2x-3+1)=0\ \ ,\ \ (2x-4)(2x-2)=0\ ,\\\\2x-4=0\ \ \to \ \ x_1=2\\\\2x-2=0\ \ \to \ \ x_2=1\\\\Otvet:\ \ x_1=2\ ,\ x_2=1\ .$