Limit of (loga (1 + x))/x
How to use the limit of Limit of (loga (1 + x))/x to solve the given limit with a logarithmic function: formula, 1 example, and its solution.
Formula
Formula
Example
Example
Solution
First write the limit part and [log2 (1 + x)].
The inner part of [log2 (1 + x)] is (1 + x).
So write x
in the denominator.
To undo the denominator x,
write x in the numerator.
Write the denominator sin x.
So [log2 (1 + x)]/(sin x)
= [(log2 (1 + x))/x]⋅[x/(sin x)].
As x → 0,
(log2 (1 + x))/x → 1/(ln 2).
As x → 0,
(sin x)/x → 1.
So x/(sin x) → 1.
Limit of (sin x)/x
[1/(ln 2)]⋅1 = 1/(ln 2)
So 1/(ln 2) is the answer.