What is the answer to 2^x+2^{x-1}+2^{x+2}=176 ?

The answer to 2^x+2^{x-1}+2^{x+2}=176 is x=5

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2^x+2^{x-1}+2^{x+2}=176

2^{x} + 2^{x - 1} + 2^{x + 2} = 176

x = 5

Solution steps

2^{x} + 2^{x - 1} + 2^{x + 2} = 176

Factor

2^{x} + 2^{x - 1} + 2^{x + 2} : 11 \cdot 2^{x - 1}

11 \cdot 2^{x - 1} = 176

Divide both sides by

11

2^{x - 1} = 16

Apply exponent rules

x - 1 = 4

Solve

x - 1 = 4 : x = 5

x = 5

- 1 \cdot 2^{x - 7} + 9 = 3

4^{- x} = 2^{x + 4}

3^{200} + 3^{200} + 3^{200} = 3^{x}

lo g_{9} (8 1^{x}) = - 2

4^{2 x} = \frac{1}{32}

What is the answer to 2^x+2^{x-1}+2^{x+2}=176 ?
The answer to 2^x+2^{x-1}+2^{x+2}=176 is x=5
Solve for x: 2^x+2^{x-1}+2^{x+2}=176
The solution is x=5