What is the answer to 2^{x+1}+2^x+2^{x-1}=112 ?

The answer to 2^{x+1}+2^x+2^{x-1}=112 is x=5

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2^{x+1}+2^x+2^{x-1}=112

2^{x + 1} + 2^{x} + 2^{x - 1} = 112

x = 5

Solution steps

2^{x + 1} + 2^{x} + 2^{x - 1} = 112

Factor

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

7 \cdot 2^{x - 1} = 112

Divide both sides by

7

2^{x - 1} = 16

Apply exponent rules

x - 1 = 4

Solve

x - 1 = 4 : x = 5

x = 5

32 = 1 6^{x - 4}

1 0^{2 x} - 2 (1 0^{x}) + 1 = 0

3^{5 x - 1} = 4^{3 x + 6}

(\frac{1}{16})^{x} = 64

1 0^{3 x} = 98

What is the answer to 2^{x+1}+2^x+2^{x-1}=112 ?
The answer to 2^{x+1}+2^x+2^{x-1}=112 is x=5
Solve for x: 2^{x+1}+2^x+2^{x-1}=112
The solution is x=5