Question

Resolver la siguiente ecuacion logaritmica. log5 (x −2) + log5 (x + 2) =1
a)x=6
b)x=2
c)x=-3
d)x=3

Answer 1

Answer:

$\tt \: log_{5}(x - 2) + log_{5}(x + 2) = 1 \\ \\ \tt \: \implies \: log_{5}(x - 2)(x + 2) = 1 \: \: \: \: \: \: \: \: \\ \\ \tt \: \implies \: {x}^{2} - {2}^{2} = {5}^{1} \\ \\ \: \tt \implies \: {x}^{2} - 4 = 5 \\ \\ \tt \implies \: {x}^{2} = 9 \\ \\ \tt \implies \ \: x = 3$