Math Help - Indeterminate Forms/L'Hospital's Rule Question (must be simple but I don't get it)

1. Indeterminate Forms/L'Hospital's Rule Question (must be simple but I don't get it)

$\lim \limits_{t \to 0}\frac{5^t - 3^t}{t}$

The solution involves L'Hospital's Rule. In the solution manual, it displays the intermediate step as:

$\lim \limits_{t \to 0}\frac{5^t ln 5 - 3^t ln 3}{1}$

Which equals:

ln 5 - ln 3 = ln 3/5

Anyone have any clue how they (specifically) managed to get the $\frac{5^t ln 5 - 3^t ln 3}{1}$? Must be an algebraic trick that isn't occurring to me...?

2. That's just a direct use of L'Hospital's rule. The derivative of the numerator is $5^{t} \ln(5) - 3^{t} \ln(3)$ and the derivative of the denominator is 1.