What is the answer to 3^{x+2}+3^{-x}=10 ?

The answer to 3^{x+2}+3^{-x}=10 is x=0,x=-2

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

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

x = 0, x = - 2

Solution steps

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

Apply exponent rules

3^{x} \cdot 3^{2} + (3^{x})^{- 1} = 10

Rewrite the equation with

3^{x} = u

u \cdot 3^{2} + (u)^{- 1} = 10

Solve

u \cdot 3^{2} + u^{- 1} = 10 : u = 1, u = \frac{1}{9}

u = 1, u = \frac{1}{9}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 1 : x = 0

Solve

3^{x} = \frac{1}{9} : x = - 2

x = 0, x = - 2

1.2 1^{x} = 100

4^{- 6} x = 1 7^{x} + 4

4^{x} \cdot 4^{2 x - 8} = 64

(\frac{1}{4})^{3 - x} = 64

2 5^{x} + 125 = 5^{x + 1}

What is the answer to 3^{x+2}+3^{-x}=10 ?
The answer to 3^{x+2}+3^{-x}=10 is x=0,x=-2
Solve for x: 3^{x+2}+3^{-x}=10
The solution is x=0,x=-2