Step-by-step Solution

Find the limit of $\frac{5^x-1}{\ln\left(1+x\right)}$ as $x$ approaches 0

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Final Answer

$\ln\left(5\right)$$\,\,\left(\approx 1.6094379124341003\right)$
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Step-by-step Solution

Problem to solve:

$\lim_{x\to0}\left(\frac{5^x-1}{\ln\left(1+x\right)}\right)$

Choose the solving method

1

If we directly evaluate the limit $\lim_{x\to 0}\left(\frac{5^x-1}{\ln\left(1+x\right)}\right)$ as $x$ tends to $0$, we can see that it gives us an indeterminate form

$\frac{0}{0}$

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$\frac{0}{0}$

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Learn how to solve limits problems step by step online. Find the limit of (5^x-1)/(ln(1+x) as x approaches 0. If we directly evaluate the limit \lim_{x\to 0}\left(\frac{5^x-1}{\ln\left(1+x\right)}\right) as x tends to 0, we can see that it gives us an indeterminate form. We can solve this limit by applying L'Hôpital's rule, which consists of calculating the derivative of both the numerator and the denominator separately. After deriving both the numerator and denominator, the limit results in. The limit of the product of a function and a constant is equal to the limit of the function, times the constant: \displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}.

Final Answer

$\ln\left(5\right)$$\,\,\left(\approx 1.6094379124341003\right)$
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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Tips on how to improve your answer:

$\lim_{x\to0}\left(\frac{5^x-1}{\ln\left(1+x\right)}\right)$

Main topic:

Limits

Related Formulas:

4. See formulas

Time to solve it:

~ 0.32 s