What is the answer to 2^x+2^{-x}= 65/8 ?

The answer to 2^x+2^{-x}= 65/8 is x=3,x=-3

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2^x+2^{-x}= 65/8

2^{x} + 2^{- x} = \frac{65}{8}

x = 3, x = - 3

Solution steps

2^{x} + 2^{- x} = \frac{65}{8}

Apply exponent rules

2^{x} + (2^{x})^{- 1} = \frac{65}{8}

Rewrite the equation with

2^{x} = u

u + (u)^{- 1} = \frac{65}{8}

Solve

u + u^{- 1} = \frac{65}{8} : u = 8, u = \frac{1}{8}

u = 8, u = \frac{1}{8}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

2^{x} = \frac{1}{8} : x = - 3

x = 3, x = - 3

7^{3 x} - 5 \cdot 7^{x + 3} + 15 = 0

- 1 0^{- 9 b} = - 92.8

e^{x} \cdot e^{x} = e^{2} x

4^{x - 1} = 8

3^{x - 3} - 1 = 5

What is the answer to 2^x+2^{-x}= 65/8 ?
The answer to 2^x+2^{-x}= 65/8 is x=3,x=-3
Solve for x: 2^x+2^{-x}= 65/8
The solution is x=3,x=-3