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Solve the logarithmic equation $\ln\left(2^x\right)=2^3$

Step-by-step Solution

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e
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ln
log
log
lim
d/dx
Dx
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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

Final Answer

$x=\frac{8}{\ln\left(2\right)}$
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Step-by-step Solution

Problem to solve:

$\ln\left(2^x\right)=2^3$

Specify the solving method

1

Calculate the power $2^3$

$\ln\left(2^x\right)=8$

Learn how to solve logarithmic equations problems step by step online.

$\ln\left(2^x\right)=8$

Unlock the first 2 steps of this solution!

Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation ln(2^x)=2^3. Calculate the power 2^3. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Eliminate the \ln\left(2\right) from the left side, multiplying both sides of the equation by the inverse of \ln\left(2\right). section:Verify that the solutions obtained are valid in the initial equation.

Final Answer

$x=\frac{8}{\ln\left(2\right)}$
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Got another answer? Verify it!

Go!
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

Useful tips on how to improve your answer:

$\ln\left(2^x\right)=2^3$

Main topic:

Logarithmic Equations

Time to solve it:

~ 0.06 s