The limit as x approaches 0 closer o 5 to the x power - 1 over x equals?

Question

2) lim 5^X -1 / x =

x->0

A) 0

b) ln 5

C) 5 ln 5

D) 1

Side note- the limit as x approaches 0 closer o 5 to the x power - 1 over x equals?

Answer 1

Since this limit results in the indeterminate form of zero/zero, L'Hopital's Rule is applicable.

L'Hopital's Rule states that the limit of an indeterminate form f(x)/g(x) can be calculated as f '(x)/g'(x)

For f(x) = 5^x - 1, f'(x) = ln(5)•5^x

For g(x) = x, g'(x) = 1