Question: Solve the logarithmic equation logâ‚…(125) = x.
1. **State the problem:** We need to solve the logarithmic equation $$\log_5(125) = x$$.
2. **Recall the definition of logarithm:** The logarithm $$\log_b(a) = c$$ means $$b^c = a$$.
3. **Apply the definition:** Here, $$b=5$$, $$a=125$$, and $$c=x$$, so we have $$5^x = 125$$.
4. **Express 125 as a power of 5:** Since $$125 = 5^3$$, the equation becomes $$5^x = 5^3$$.
5. **Equate the exponents:** Because the bases are the same and non-zero, $$x = 3$$.
6. **Conclusion:** The solution to the equation $$\log_5(125) = x$$ is $$x = 3$$.
**Answer:** c.) $$x = 3$$