What is the answer to 2^{x+1}+2^{x-1}+2^x=28 ?

The answer to 2^{x+1}+2^{x-1}+2^x=28 is x=3

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2^{x+1}+2^{x-1}+2^x=28

2^{x + 1} + 2^{x - 1} + 2^{x} = 28

x = 3

Solution steps

2^{x + 1} + 2^{x - 1} + 2^{x} = 28

Factor

2^{x + 1} + 2^{x - 1} + 2^{x} : 7 \cdot 2^{x - 1}

7 \cdot 2^{x - 1} = 28

Divide both sides by

7

2^{x - 1} = 4

Apply exponent rules

x - 1 = 2

Solve

x - 1 = 2 : x = 3

x = 3

2 5^{x} + 5^{1 + 2 x} = 20

3^{2 x - 1} = 1

7 (8^{x + 1}) = 448

e^{8 x} = 0

\frac{4}{1 0 ^{(x - 1)} - 9} = 22

What is the answer to 2^{x+1}+2^{x-1}+2^x=28 ?
The answer to 2^{x+1}+2^{x-1}+2^x=28 is x=3
Solve for x: 2^{x+1}+2^{x-1}+2^x=28
The solution is x=3