ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Solve the exponential equation $2^{\left(x-1\right)}+2^x+2^{\left(x+1\right)}=28$

Go!
Symbolic mode
Text mode
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

##  Final answer to the problem

$x=3$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Solve for x
• Find the derivative using the definition
• Solve by quadratic formula (general formula)
• Simplify
• Find the integral
• Find the derivative
• Factor
• Factor by completing the square
• Find the roots
Can't find a method? Tell us so we can add it.
1

Apply the property of the product of two powers of the same base in reverse: $a^{m+n}=a^m\cdot a^n$

$2^{-1}2^x+2^x+2\cdot 2^x=28$

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

$2^{-1}2^x+2^x+2\cdot 2^x=28$

Learn how to solve exponential equations problems step by step online. Solve the exponential equation 2^(x-1)+2^x2^(x+1)=28. Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Combining like terms 2^x and 2\cdot 2^x. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Multiplying the fraction by 2^x.

##  Final answer to the problem

$x=3$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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

###  Main Topic: Exponential Equations

Exponential equations are those where the unknown appears only in the exponents of powers of constant bases.