If $$5^{2x-1}=1/(125)^{x-3}$$, find $$x$$.
If $$5^{2x-1}=1/(125)^{x-3}$$, find $$x$$.
Let us simplify the given expression,
$$5^{2x-1}=1/(5^{3})^{x-3}$$
$$5^{2x-1}=1/5^{3x-9}$$
$$5^{2x-1}=5^{3x+9}$$
Now by comparing the powers, we get
$$2x-1=-3x+9$$
$$2x+3x=9+1$$
$$6x=10$$
$$x=10/5$$
$$=2$$