COPY - Solve for the variable 125^2x=25^3x-100 x=5 x=-5 x=-40 None of the above x=40 x=-50

To solve the equation $125^{2x}=25^{3x-100}$, we can rewrite both sides of the equation with the same base.<br /><br />$125 = 5^3$ and $25 = 5^2$, so the equation becomes:<br /><br />$(5^3)^{2x} = (5^2)^{3x-100}$<br /><br />Simplifying, we get:<br /><br />$5^{6x} = 5^{6x-200}$<br /><br />Since the bases are the same, we can set the exponents equal to each other:<br /><br />$6x = 6x - 200$<br /><br />Solving for $x$, we get:<br /><br />$0 = -200$<br /><br />This is not possible, so there is no solution for the variable $x$ in the given equation.<br /><br />Therefore, the correct answer is "None of the above".