Im really confused with the way my texbook explains the answer to this question:

lim as x approaches 0 of (5^x- 3^x)/x

So clearly thats impossible since there cant be a 0 in the denomintor so we use L'hospital's rule. Now the back of my textbook uses ln and this is where it got me confused:

lim (5^x- 3^x)/x = lim (5^xln5- 3^xln3)/1

I thought the general log rule was ln5^x = xln5 not 5^xln5 ???