Answer: [tex]x=11[/tex]
Step-by-step explanation:
Remembert that, by definition:
[tex]log_b(x)=y[/tex] → [tex]b^y=x[/tex]
Then, you can rewrite [tex]log_4(2x-6)=2[/tex] in exponential form:
[tex]4^2=2x-6[/tex]
Now you can solve for the variable "x":
Add 6 to both sides of the equation:
[tex]4^2+6=2x-6+6[/tex]
[tex]22=2x[/tex]
And finally you must divide both sides of the equation by 2, then:
[tex]\frac{22}{2}=\frac{2x}{2}\\\\x=11[/tex]
