Limit of log(1+x)/x as x approaches 0

The limit of log(1+x)/x as x approaches 0 is equal to 1. The limx -> 0 (log(1 + x))/x formula is given by

$\lim\limits_{x \to 0} \dfrac{\log(1+x)}{x}=1$.

In this post, we will learn to prove the limit of log(1+x)/x when x tends to zero.

Limx → 0 log(1 + x)/x

Note that the given limit can be written as

$\lim\limits_{x \to 0} \dfrac{1}{x} \log(1+x)$

= $\lim\limits_{x \to 0} \log(1+x)^{\frac{1}{x}}$ by the logarithm rules

= $\log \lim\limits_{x \to 0} (1+x)^{\frac{1}{x}}$ using the property limx→0 log(f(x)) = log limx→0 f(x).

= $\log e$ by the limit formula limx→0 (1+x)1/x = e.

= 1 if the base is e.

So the limit of log(1+x)/x is equal to 1 when x→0, provided that the logarithm base is e.

More Limits:

Limit of x/sinx when x→0

Limit of sinx/x when x→∞

Limit of sin(1/x) when x→0

Limit of sin3x/sin2x when x→0

Limit of tanx/x when x→0

Limit of (cosx-1)/x when x→0

Limit of (ex-1)/x when x→0

FAQs

Q1: What is the limit of log(1+x)/x when x tends to 0?

Answer: The limit of log(1+x)/x when x tends to 0 is equal to 1, that is, limx→0 log(1 + x)/x =1.