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

To solve the equation $5^{x}=25^{3x-100}$, we can rewrite $25$ as $5^2$ and then use the property of exponents that states $(a^m)^n = a^{mn}$.<br /><br />So, $5^{x} = (5^2)^{3x-100} = 5^{2(3x-100)} = 5^{6x-200}$.<br /><br />Since the bases are the same, we can set the exponents equal to each other:<br /><br />$x = 6x - 200$<br /><br />Solving for $x$, we get:<br /><br />$x - 6x = -200$<br /><br />$-5x = -200$<br /><br />$x = 40$<br /><br />Therefore, the correct answer is $x=40$.