What is the answer to 2^{x+1}+2^{x-1}=20 ?

The answer to 2^{x+1}+2^{x-1}=20 is x=3

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2^{x+1}+2^{x-1}=20

2^{x + 1} + 2^{x - 1} = 20

x = 3

Solution steps

2^{x + 1} + 2^{x - 1} = 20

Factor

2^{x + 1} + 2^{x - 1} : 5 \cdot 2^{x - 1}

5 \cdot 2^{x - 1} = 20

Divide both sides by

5

2^{x - 1} = 4

Apply exponent rules

x - 1 = 2

Solve

x - 1 = 2 : x = 3

x = 3

e^{2 x} - e^{x} - 12 = 0

e^{2 x + 1} - 3 = 0

20 (7^{2 x}) = 40 (5^{3 x + 1})

7^{x + 2} = 98

x, e^{a x} = C e^{b x}

What is the answer to 2^{x+1}+2^{x-1}=20 ?
The answer to 2^{x+1}+2^{x-1}=20 is x=3
Solve for x: 2^{x+1}+2^{x-1}=20
The solution is x=3