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

3 6^{x} + 4 2^{x} = 4 9^{x}

5 \cdot 1 8^{6 x} = 26

5^{x} = 4

6^{x} = 216

3^{2 x + 2} + 3^{x + 3} - 10 = 0

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