Question

Sendo o logaritmo de B na base a² igual x e o logaritmo de B na base 1/a igual a y, então:
A) x . y² = 1
B) x² . y = 1
C) y + 2x = 0
D) x + 2y = 0

Answer 1

• $\log_{a}b=x$ é o mesmo que $a^x=b$
• $\frac{1}{a}=a^{-1}$
• $(a^b)^c=a^{b.c}$

$\log_{a^2}B=x\\\\(a^2)^x=B\\\\\\\log_{\frac{1}{a}}B=y\\\\(a^{-1})^y=B\\\\\\(a^2)^x=(a^{-1})^y\\\\a^{2x}=a^{-y}\\\\2x=-y\\\\2x+y=0$