Question

preciso com cálculo!!!!!!!

Answer 1

• A ↔

$\sf log _x\left8\right\\\\\\{Reescreva\:}8{\:utilizando\:potencias:}\quad 8=2^3\\\\\\=log _x\left(2^3\right)\\\\\\{Aplicar\:as\:propriedades\:dos\:logaritmos}:\quad log _a\left(x^b\right)=b\cdot log _a\left(x\right)\\\\\\log _x\left(2^3\right)=3~log _x\left(2\right)\\\\\\\to \boxed{\sf \red{=3 ~log _x\left(2\right)}}$

• B ↔

$\sf log _7\left(x^2-4\right)\\\\\\Fatore \ => \ x^2-4\\\\\\\to \boxed{\sf \green{=log _7\left(\left(x+2\right)\left(x-2\right)\right)}}$

• C ↔

$\sf log _{x-1}\left(x^2\right)\\\\\\{Aplicar\:as\:propriedades\:dos\:logaritmos}\:~log _a\left(x^b\right)=b\cdot ~log _a\left(x\right){\:assumindo\:que\:}x\:\ge \:0\\\\\\\to \boxed{\sf \orange{=2~log _{x-1}\left(x\right)}}$

• D ↔

$\sf log _{x^2-1}\left(x^2-2\right)\\\\\\Fatore \ => \ x^2-1\\\\\\\to \boxed{\sf \blue{=log _{\left(x+1\right)\left(x-1\right)}\left(x^2-2\right)}}$