Question

log10 (x-1)+ log10 (x+1)=log102. помогите решить​

Answer 1

$log_{10}(x-1)+log_{10}(x+1)=log_{10}2\; \; ,\; \; \; ODZ:\; \left \{ {{x-1>\; 0} \atop {x+1>0}} \right. \; ,\; \; x>1\\\\lg(x^2-1)=lg2\\\\x^2-1=2\\\\x^2-3=0\\\\(x-\sqrt3)(x+\sqrt3)=0\\\\x_1=-\sqrt3<1\; ,\; \; x_2=\sqrt3\in ODZ\\\\Otvet:\; \; x=\sqrt3\; .$