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

Step-by-step Solution

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Final answer to the problem

$x=3$
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Step-by-step Solution

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

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

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

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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

$x=3$

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Function Plot

Plotting: $2^{\left(x-1\right)}+2^x+2^{\left(x+1\right)}-28$

SnapXam A2
Answer Assistant

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Got a different answer? Verify it!

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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

How to improve your answer:

Main Topic: Exponential Equations

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

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