Using logarithms property of log(x)+log(y)=log(xy)
so here, you can sum the equation to;
[tex]log((x+6)*(x-6))=2[/tex]
so you can simply say that;
[tex] log_{8}((x+6)( x-6))=2 [/tex]
and by multiplying (x+6)*(x-6)
[tex]log_{8}(x^2-36)=2[/tex]
and as you know also that;
[tex] a^{b}=c [/tex] is same as [tex]log _{a}c=b [/tex]
so you can simply state it as;
[tex]8^2=x^2-36
64=x^2-36
64+36=x^2
x^2=100
x=10[/tex]
And you can check your work by substituting with 10 instead of x in the original function.
Hope this helps!
