1. The problem is to understand and apply the change of base formula for logarithms. 2. The change of base formula states that for any positive numbers $a$, $b$, and $c$ (with $a \neq 1$ and $b \neq 1$), $$\log_b a = \frac{\log_c a}{\log_c b}$$ This means you can convert a logarithm from base $b$ to any other base $c$. 3. This formula is useful because calculators typically only compute logarithms in base 10 or base $e$ (natural logarithm). 4. For example, to compute $\log_2 8$ using base 10 logarithms: $$\log_2 8 = \frac{\log_{10} 8}{\log_{10} 2}$$ 5. Calculate each logarithm: $$\log_{10} 8 \approx 0.9031$$ $$\log_{10} 2 \approx 0.3010$$ 6. Divide the results: $$\frac{0.9031}{0.3010} = 3$$ 7. Therefore, $\log_2 8 = 3$, which matches the fact that $2^3 = 8$. This demonstrates how to use the change of base formula to evaluate logarithms with any base.