Answer:
x = 1
Explanation:
To solve for x in the equation,
[tex]4^{3x-3}=8^{4x-4}[/tex]We write each side as
[tex]\begin{gathered} 4^{3x-3}=(2^2)^{3x-3} \\ 8^{4x-4}=\mleft(2^3\mright)^{\mleft\{4x-4\mright\}} \end{gathered}[/tex]which gives
[tex](2^2)^{3x-3}=(2^3)^{\{4x-4\}}[/tex]Now, using the property that
[tex](A^x)^y=A^{xy}[/tex]we rewrite the above as
[tex]2^{2(3x-3)}=2^{3\{4x-4\}}[/tex]Which implies
[tex]2(3x-3)=3(4x-4)_{}[/tex]Expanding the equation gives
[tex]6x-6=12x-12[/tex]Adding 6 to both sides gives
[tex]6x=12x-12+6[/tex][tex]6x=12x-6[/tex]subtracting 12x from both sides gives
[tex]6x-12x=-6[/tex][tex]-6x=-6[/tex]Finally, dividing both sides by -6 gives
[tex]x=1[/tex]which is our answer!
