Question

Usando a definição de logaritmos calcule : log( base 1/5) 125

Answer 1

log(1/5) 125 = x =
(1/5)^x = 125
(5-¹)^x = 5³
-x = 3 *(-1)
x = -3

log(1/5) 125 = -3

Answer 2

$\sf log _{\dfrac{1}{5}}\left(125\right)\\\\\\{Aplique\:as\:propriedades\:dos\:logaritmos}:\quad log _{\dfrac{1}{a}}\left(x\right)=-log _a\left(x\right)\\\\\\log _{\dfrac{1}{5}}\left(125\right)=-log _5\left(125\right)\\\\\\{Fatore\:o\:número:\:}\:125=5^3\\\\\\=-log _5\left(5^3\right)\\\\\\{Aplique\:as\:propriedades\:dos\:logaritmos}:\quad \log _a\left(a^x\right)=x\\\\\\log _5\left(5^3\right)=3\\\\\\\to \boxed{\sf \blue{x=-3}}$