решить логарифмическое уравнение:log_{5}(x^2+8)-log_{5}(x+1)=3log_{5}2

$log_{5}(x^2+8)=log_{5}(x+1)+3log_{5}2$

$log_{5}(x^2+8)=log_{5}8(x+1)$

0}} \right." alt="\left \{ {{x^2+8=8(x+1)} \atop {x+1>0}} \right." align="absmiddle" class="latex-formula">

0}} \right." alt="\left \{ {{x^2-8x=0} \atop {x+1>0}} \right." align="absmiddle" class="latex-formula">

0}} \right." alt="\left \{ {{x(x-8)=0} \atop {x+1>0}} \right." align="absmiddle" class="latex-formula">

-1}} \right." alt="\left \{ {{x_1=0, x_2=8} \atop {x>-1}} \right." align="absmiddle" class="latex-formula">

Отсюда х=0 или х=8. Ответ:0; 8.