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

## Step-by-step Solution

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###  Videos

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

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Calculate the power $2^3$

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

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

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

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). Divide both sides of the equation by \ln\left(2\right). Simplifying the quotients.

$x=\frac{8}{\ln\left(2\right)}$

$x=11.5416$

##  Explore different ways to solve this problem

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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

### Main Topic: Logarithmic Equations

Are those equations in which the unknown variable appears within a logarithm.

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