When working on exponential and logarithmic equations, I’ve found some useful tips over the years. Here’s what I think works best:

1. Know the Basics: First, it’s important to understand how exponents and logarithms are related. Remember this key point: if (y = b^x), then (x = \log_b(y)). This connection helps you switch between the two types easily.

2. Learn the Rules: Get to know the rules for logarithms, like how to handle products, divisions, and powers. For example:

   • (\log_b(MN) = \log_b(M) + \log_b(N))
   • (\log_b\left(\frac{M}{N}\right) = \log_b(M) - \log_b(N))
   • (\log_b(M^k) = k \cdot \log_b(M))

   Using these rules can help you make tough problems simpler.

3. Isolate the Terms: When solving equations, try to get the exponential or logarithmic part alone on one side. This may mean doing some algebra to rearrange the equation.

4. Switch Forms: If you get stuck, try changing the equation from exponential to logarithmic or the other way around. This can help you see how to isolate the variable better.

5. Check Your Work: After you think you’ve found an answer, put it back into the original equation. Since exponential and logarithmic functions can be tricky, checking helps you catch mistakes.

6. Try Graphing: If nothing else works, consider graphing the functions. Sometimes, you can see where they cross or how they behave more clearly this way.

These strategies have definitely made working with exponential and logarithmic functions a lot easier and less scary!