We have this exponential equation here:
[tex]64^{2x-1}=16^{4x-3}[/tex]Let's create equivalent expressions with the same base, 2.
[tex]2^{6(2x-1)}=2^{4(4x-3)}[/tex]Since they have equal bases we can set the exponents equal to each other.
[tex]6(2x-1)=4(4x-3)[/tex]Simplify the equation.
[tex]12x-6=16x-12[/tex]Solve for x.
[tex]\begin{gathered} 6=4x \\ x=\frac{6}{4}=\frac{3}{2} \end{gathered}[/tex]The answer is x = 3/2.
