To calculate $\log_{12}{24}$, use the change of base formula:

$\log_{b}{x} = \frac{\log{x}}{\log{b}}$

Here, $b = 12$ and $x = 24$. Using this formula:

$\log_{12}{24} = \frac{\log{24}}{\log{12}}$

Now, calculating step by step using a calculator:

1. Calculate $\log{24}$:
   $\log{24} \approx 1.3802$

2. Calculate $\log{12}$:
   $\log{12} \approx 1.0792$

3. Divide the two results:
   $\frac{\log{24}}{\log{12}} = \frac{1.3802}{1.0792} \approx 1.2789$

Thus, $\log_{12}{24} \approx 1.2789$ rounded to four decimal places.

Would you like further clarification or have questions about this process? Here are five related questions to deepen your understanding:

1. How can the change of base formula be derived?
2. Can the base of a logarithm be any number?
3. How would $\log_{12}{24}$ differ if using natural logarithms ($\ln$) instead of common logarithms?
4. Why do logarithms behave differently with respect to base changes?
5. How is the change of base formula applied in solving real-world problems?

Tip: Always double-check your logarithmic calculations to avoid errors in rounding or using the calculator.