What is the answer to 2^{x+1}+2^x+2^{x-1}=14 ?

The answer to 2^{x+1}+2^x+2^{x-1}=14 is x=2

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2^{x+1}+2^x+2^{x-1}=14

2^{x + 1} + 2^{x} + 2^{x - 1} = 14

x = 2

Solution steps

2^{x + 1} + 2^{x} + 2^{x - 1} = 14

Factor

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

7 \cdot 2^{x - 1} = 14

Divide both sides by

7

2^{x - 1} = 2

Apply exponent rules

x - 1 = 1

Solve

x - 1 = 1 : x = 2

x = 2

7^{x} = 4

6 (6^{2 x}) - 37 (6^{x}) + 6 = 0

e^{2 x} = 3 e^{x}

10 \cdot 3^{\frac{5 t}{4}} = 800

1^{x} = - 1

What is the answer to 2^{x+1}+2^x+2^{x-1}=14 ?
The answer to 2^{x+1}+2^x+2^{x-1}=14 is x=2
Solve for x: 2^{x+1}+2^x+2^{x-1}=14
The solution is x=2