Question: User: 125=5^x
1. **State the problem:** Solve the equation $$125 = 5^x$$ for $$x$$.
2. **Recall the formula and rules:** We know that $$125$$ can be expressed as a power of $$5$$ because $$125 = 5^3$$.
3. **Rewrite the equation:** Substitute $$125$$ with $$5^3$$:
$$5^3 = 5^x$$
4. **Apply the rule of equality of exponents:** If $$a^m = a^n$$ and $$a > 0$$, then $$m = n$$.
5. **Set the exponents equal:**
$$3 = x$$
6. **Final answer:**
$$x = 3$$