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

To solve the equation \( 3^{x}-3^{x-2}=24 \), start by rewriting \( 3^{x-2} \) as \( \frac{3^x}{9} \). This transforms the equation into \[ 3^x - \frac{3^x}{9} = 24. \] Now, factor \( 3^x \): \[ 3^x \left(1 - \frac{1}{9}\right) = 24. \] Simplifying the term in the parentheses gives us \[ 3^x \left(\frac{8}{9}\right) = 24. \] Multiplying both sides by \( \frac{9}{8} \) to isolate \( 3^x \): \[ 3^x = 24 \cdot \frac{9}{8} = 27. \] Since \( 27 = 3^3 \), it follows that \( x = 3 \). So, the solution to the equation is \( x = 3 \).