Find the limit of (10^x - 5^x)/x as x approaches 0

Question

without using l'Hospital's rule

Answer 1

The derivative of a^x is a^x*ln a
The numerator's derivative is
1n 10*10^x - ln 5*5^x
which at x = 0 equals ln 10 - 1n 5 = ln 2 = 0.693
Th derivative of the denominator is a= 1.
L'Hopital's rule gives you a limit of 0.693/1 = 0.693 for the derivative