When working on exponential and logarithmic equations in Year 13, it's easy to make some mistakes. Here are a few common errors to watch out for:

1. Confusing the Rules:

   • It's simple to mix up the rules for exponents and logarithms. For example, remember that if you have $a^{m+n}$, it equals $a^m \cdot a^n$. But $a^{m/n}$ is not the same as $a^m/a^n$. Keep these rules clear!

2. Forgetting the Domain:

   • Don't forget that logarithmic functions only work for numbers greater than zero ($x > 0$). If you overlook this, you might find answers that don't make sense.

3. Misreading Equations:

   • If you see an equation like $e^x = 3$, it’s important to take the natural log of both sides. Make sure to use $ln$ properly to solve for $x$.

4. Not Checking Your Answers:

   • After solving your equations, always check your answers by plugging them back into the original equation. Some answers might not actually work, especially if you squared both sides earlier.

5. Forgetting the Base:

   • When dealing with logarithms, remember that the base matters. For example, $log_2(x)$ is different from $log_{10}(x)$.

By paying attention to these common mistakes, you can improve your understanding of these interesting math topics!