An algebra problem by Michael Wang

Using the laws of logarithms, you get $\log_b \frac{m}{n}=\frac{\log_b m}{\log_b n}$ . Using this law in reverse yields $\frac{\log_b m}{\log_b n}=\log_b \frac{m}{n}$ . Plugging in the numbers on the left hand side results $\frac{\log_2 24}{\log_2 3}=\log_2 \frac{24}{3}$ . Solving gives $\log_2 8=\log_5 n$ , or $3=\log_5 n$ . Using the definition of logarithms yields $5^3=n$ , or $n=125$ .