we can use formula
[tex]y=alog_b(x+c)+d[/tex]
We can see that each options has base=2
so, we can take b=2
[tex]y=alog_2(x+c)+d[/tex]
and each options has added 6
so, d=6
[tex]y=alog_2(x+c)+6[/tex]
now, we can select each points
At x=0 , y=4
[tex]4=alog_2(0+c)+6[/tex]
[tex]-2=alog_2(c)[/tex]
At x=-3 , y=6:
[tex]6=alog_2(-3+c)+6[/tex]
[tex]alog_2(-3+c)=0[/tex]
Since, 'a' can not be 0
so,
[tex]log_2(-3+c)=[/tex]
we can solve for c
we can take exponent over 2
[tex]2^{log_2(-3+c)}=2^0[/tex]
[tex]-3+c=1[/tex]
[tex]c=4[/tex]
now, we can plug it back
[tex]-2=alog_2(4)[/tex]
and then we can solve for a
[tex]-2=alog_2(2^2)[/tex]
[tex]-2=2alog_2(2)[/tex]
[tex]2a=-2[/tex]
[tex]a=-1[/tex]
now, we can plug these values
and we get
[tex]y=-log_2(x+4)+6[/tex].................Answer
