Let’s take a closer look at the questions one by one!

A1. Solve the equation:
$3^{5 + x} = 9$

We start by expressing 9 as a power of 3:
$9 = 3^2$

So the equation becomes:
$3^{5 + x} = 3^2$

Since the bases are equal, the exponents must be equal:
$5 + x = 2$

Solving for $x$:
$x = 2 - 5 = -3$

Answer: $x = -3$

Would you like me to keep going with the rest of the problems? Let me know!

Here are five questions related to the first one:

1. How do we solve exponential equations with different bases?
2. What happens if the equation involves different exponents on both sides with the same base?
3. How do we handle equations where the bases cannot easily be made equal?
4. What is the significance of taking the logarithm when solving exponential equations?
5. How can we check our solution once we find the value of $x$?

Tip: When solving exponential equations, always check if you can rewrite the numbers as powers of the same base — it simplifies things a lot!