Question

Resolva as equações. a) log3 (5x+10) - log3(x-2) = 3

Answer 1

Das propriedades dos logaritmos:

$\log_{a}{P} - \log_{a}{Q}=\frac{\log_{a}{P}}{\log_{a}{Q}}$

Aplicando no nosso problema

$\log_{3}{(5X+10)} - \log_{3}{(X-2)}=\frac{\log_{3}{(5X+10)}}{\log_{3}{(X-2)}}$

entao

$\log_{3}{(5X+10)} - \log_{3}{(X-2)}=3\Rightarrow \log_{3}\frac{(5X+10)}{(X-2)}=3$

Tambem dos logaritmos temos $\log_{a}{b}=c\Rightarrow a^{c}=b$

Sendo assim

$\log_{3}\frac{(5X+10)}{(X-2)}=3\Rightarrow \frac{(5X+10)}{(X-2)}=3^{3}$

$\frac{(5X+10)}{(X-2)}=3^{3}$

5X + 10 = 27X - 54

X = 64/22

X = 32/11