Answer:
The correct option is D.
Step-by-step explanation:
The given equation is
[tex]log_{2x-6}(256)=4[/tex]
This equation can be written as
[tex](2x-6)^{log_{2x-6}(256)}=(2x-6)^4[/tex]
[tex]256=(2x-6)^4[/tex] [tex][\because a^{log_ax}=x][/tex]
Taking 4th root both sides.
[tex]4=(2x-6)[/tex]
[tex]4+6=2x[/tex]
[tex]10=2x[/tex]
[tex]5=x[/tex]
The value of x is 5.
Therefore correct option is D.
