What is the answer to 3^{x+2}+3^{2-x}=82 ?

The answer to 3^{x+2}+3^{2-x}=82 is x=2,x=-2

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3^{x+2}+3^{2-x}=82

3^{x + 2} + 3^{2 - x} = 82

x = 2, x = - 2

Solution steps

3^{x + 2} + 3^{2 - x} = 82

Apply exponent rules

3^{x} \cdot 3^{2} + (3^{x})^{- 1} \cdot 3^{2} = 82

Rewrite the equation with

3^{x} = u

u \cdot 3^{2} + (u)^{- 1} \cdot 3^{2} = 82

Solve

u \cdot 3^{2} + u^{- 1} \cdot 3^{2} = 82 : u = 9, u = \frac{1}{9}

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

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 9 : x = 2

Solve

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

x = 2, x = - 2

2 0^{x - 9} = 12

1 0^{\frac{3 x - 1}{2 x + 1}} = 100

0.2 e^{4 x} - 0.1 e^{- 3 x} = 0

(1 4^{3 x + 1}) (8^{2 x + 3}) = 7

5^{x} = 22

What is the answer to 3^{x+2}+3^{2-x}=82 ?
The answer to 3^{x+2}+3^{2-x}=82 is x=2,x=-2
Solve for x: 3^{x+2}+3^{2-x}=82
The solution is x=2,x=-2