a) \( 3^{x}-3^{x-2}=24 \)

Let's have some fun with this equation! We can start by rewriting \( 3^{x-2} \) as \( \frac{3^{x}}{3^{2}} \) or \( \frac{3^{x}}{9} \). This gives us: \[ 3^x - \frac{3^x}{9} = 24 \] Now, combining like terms, we can factor out \( 3^x \): \[ 3^x \left(1 - \frac{1}{9}\right) = 24 \] This simplifies to: \[ 3^x \left(\frac{8}{9}\right) = 24 \] Multiplying both sides by \( \frac{9}{8} \), we obtain: \[ 3^x = 24 \cdot \frac{9}{8} = 27 \] Now we can express 27 as a power of 3: \[ 3^x = 3^3 \] Thus, \( x = 3 \). Voilà! The solution is \( x = 3 \). Got your thinking cap on? Let’s spice up our equation-solving skills here and keep that math magic alive!