4) \( \begin{aligned} 5^{x} & =45 \\ 5^{x} & =5\end{aligned} \)

To solve \( 5^{x} = 45 \), you can take the logarithm of both sides: \( x \log(5) = \log(45) \). Then, isolate \( x \) by dividing both sides by \( \log(5) \): \( x = \frac{\log(45)}{\log(5)} \). Now, let's tackle the second equation. Since \( 5^{x} = 5 \), it follows that \( x = 1 \) because any base raised to the power of 1 equals itself. So the solutions are \( x = \frac{\log(45)}{\log(5)} \) for the first equation and \( x = 1 \) for the second! Quantifying it can lead to exciting math adventures!