Answer:
C
Step-by-step explanation:
A. False.
The equation [tex]\log_4(x+6)=2[/tex] is equivalent to the equation
[tex]4^{\log _4(x+6)}=4^2[/tex]
The right side is [tex]4^2[/tex] not [tex]2^2[/tex]
B. False.
The equation [tex]\log_4(x+6)=2[/tex] is equivalent to the equation
[tex]4^{\log _4(x+6)}=4^2[/tex]
The right side is [tex]4^2[/tex] not [tex]4^4[/tex]
C. True.
Since [tex]\log_416=\log_44^2=2\log_44=2\cdot 1=2,[/tex] then the equation [tex]\log_4(x+6)=2[/tex] is equivalent to the equation [tex]\log_4(x+6)=\log _416[/tex]
D. False.
Since [tex]\log_216=\log_22^4=4\log_22=4\cdot 1=4,[/tex] this option is false
