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

We're asked to find:



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



Which equals:

ln 5 - ln 3 = ln 3/5

Anyone have any clue how they (specifically) managed to get the ? Must be an algebraic trick that isn't occurring to me...?

Thanks in advance!

That's just a direct use of L'Hospital's rule. The derivative of the numerator is and the derivative of the denominator is 1.