which of the following shows the equation $log_4(x + 6)=2$ rewritten using logarithms?\n$4^{log_4(x +…

which of the following shows the equation $log_4(x + 6)=2$ rewritten using logarithms?\n$4^{log_4(x + 6)}=2^2$\n$4^{log_4(x + 6)}=4^4$\n$log_4(x + 6)=log_416$\n$log_4(x + 6)=log_216$

which of the following shows the equation $log_4(x + 6)=2$ rewritten using logarithms?\n$4^{log_4(x + 6)}=2^2$\n$4^{log_4(x + 6)}=4^4$\n$log_4(x + 6)=log_416$\n$log_4(x + 6)=log_216$

Answer

Explanation:

Step1: Usar la definición de logaritmo

Según la definición $y = \log_a x$ se puede reescribir como $a^y=x$. Para $\log_4(x + 6)=2$, tenemos $4^2=x + 6$, es decir $x+6 = 16$.

Step2: Aplicar la propiedad de los logaritmos

Si $x+6 = 16$, entonces $\log_4(x + 6)=\log_4 16$ (ya que si $a=b$, entonces $\log_c a=\log_c b$ para $c>0,c\neq1$).

Answer:

$\log_4(x + 6)=\log_4 16$