What is the answer to 2^{x+2}+2^{x+1}+2^x=896 ?

The answer to 2^{x+2}+2^{x+1}+2^x=896 is x=7

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2^{x+2}+2^{x+1}+2^x=896

2^{x + 2} + 2^{x + 1} + 2^{x} = 896

x = 7

Solution steps

2^{x + 2} + 2^{x + 1} + 2^{x} = 896

Factor

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

7 \cdot 2^{x} = 896

Divide both sides by

7

2^{x} = 128

Apply exponent rules

x = 7

4^{x + 3} = 8^{3 x - 4}

3^{2 x - 3} = 6

2^{x - 3} = 5

9 (5^{x}) = 8^{x + 4}

5^{6 x + 1} - 6 \cdot 5^{3 x} + 1 = 0

What is the answer to 2^{x+2}+2^{x+1}+2^x=896 ?
The answer to 2^{x+2}+2^{x+1}+2^x=896 is x=7
Solve for x: 2^{x+2}+2^{x+1}+2^x=896
The solution is x=7