Answer: Third option.
Step-by-step explanation:
We need to remember that:
[tex]a^m=a^n\\\\m=n[/tex]
In this case, given this expression:
[tex]4^x[/tex][tex]=8^{( x- 1)}[/tex]
We need to descompose 4 and 8 into their prime factors:
[tex]4=2*2=2^2[/tex]
[tex]8=2*2*2=2^3[/tex]
Rewriting the expression:
[tex]2^{2x}[/tex][tex]=2^{3(x - 1) }[/tex]
Then:
[tex]2x = 3(x - 1)[/tex]
Finally, applying Distributive property on the right side and solving for "x", we get:
[tex]2x=3x-3\\\\3=3x-2x\\\\x=3[/tex]
