What is the answer to 3^x+3^{-x}= 10/3 ?

The answer to 3^x+3^{-x}= 10/3 is x=1,x=-1

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3^x+3^{-x}= 10/3

3^{x} + 3^{- x} = \frac{10}{3}

x = 1, x = - 1

Solution steps

3^{x} + 3^{- x} = \frac{10}{3}

Apply exponent rules

3^{x} + (3^{x})^{- 1} = \frac{10}{3}

Rewrite the equation with

3^{x} = u

u + (u)^{- 1} = \frac{10}{3}

Solve

u + u^{- 1} = \frac{10}{3} : u = 3, u = \frac{1}{3}

u = 3, u = \frac{1}{3}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = 1

Solve

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

x = 1, x = - 1

3^{x} = 1

9^{x} + 1 5^{x} = 2 5^{x}

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

7^{x^{2} - 13 x + 45} = 16807

1. 2^{x} = 10

What is the answer to 3^x+3^{-x}= 10/3 ?
The answer to 3^x+3^{-x}= 10/3 is x=1,x=-1
Solve for x: 3^x+3^{-x}= 10/3
The solution is x=1,x=-1