Answer:
x=4
Step-by-step explanation:
All right. All the bases are the same (8) so you can basically just do some rearranging and it'll be a simple equation. First thing to do is make sure you move the 2 by the first logarithm to the exponent, changing it to [tex]log_8(x)^2[/tex]
Now your equation should look like
[tex]log_8(x)^2=log_88+log_8(x-2)\\[/tex]
Now since the bases are the same, you just use the numbers on top (there's a more technical term escaping me, right now.
Remember that adding logs together is equivalent to multiplication.
[tex]log_8(x)^2=log_88+log_8(x-2)\\x^2=8(x-2)\\x^2=8x-16\\x^2-8x+16=0\\(x-4)(x-4)=0\\x=4[/tex]
x=4
