What is the answer to 2^{(x-3)}+2^{(x-1)}+2^x=52 ?

The answer to 2^{(x-3)}+2^{(x-1)}+2^x=52 is x=5

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2^{(x-3)}+2^{(x-1)}+2^x=52

2^{(x - 3)} + 2^{(x - 1)} + 2^{x} = 52

x = 5

Solution steps

2^{(x - 3)} + 2^{(x - 1)} + 2^{x} = 52

Factor

2^{x - 3} + 2^{x - 1} + 2^{x} : 13 \cdot 2^{x - 3}

13 \cdot 2^{x - 3} = 52

Divide both sides by

13

2^{x - 3} = 4

Apply exponent rules

x - 3 = 2

Solve

x - 3 = 2 : x = 5

x = 5

4^{y} = 32

2^{x^{2}} = 512

2^{6 x + 12} = 8^{2 x + 4}

2^{x - 2} - 3 \cdot 2^{x} + 8 = 0

2^{x^{2} + 7 x - 38} = 6 4^{x - 6}

What is the answer to 2^{(x-3)}+2^{(x-1)}+2^x=52 ?
The answer to 2^{(x-3)}+2^{(x-1)}+2^x=52 is x=5
Solve for x: 2^{(x-3)}+2^{(x-1)}+2^x=52
The solution is x=5