1. **Stating the problem:** Solve the logarithmic equation $$\log_5 5 - 20c + \log_3 2 = \log_5 20$$ 2. **Recall logarithm properties:** - $\log_a a = 1$ for any base $a$. - $\log_a x + \log_a y = \log_a (xy)$ if the bases are the same. - We can isolate terms and solve for $c$. 3. **Evaluate known logs:** - $\log_5 5 = 1$ 4. **Rewrite the equation:** $$1 - 20c + \log_3 2 = \log_5 20$$ 5. **Isolate $c$:** $$-20c = \log_5 20 - 1 - \log_3 2$$ 6. **Divide both sides by $-20$:** $$c = \frac{1 + \log_3 2 - \log_5 20}{20}$$ 7. **Final answer:** $$c = \frac{1 + \log_3 2 - \log_5 20}{20}$$ This expresses $c$ in terms of logarithms with bases 3 and 5.