What is the answer to 3^{x+1}+3^{2-x}=28 ?

The answer to 3^{x+1}+3^{2-x}=28 is x=2,x=-1

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3^{x+1}+3^{2-x}=28

3^{x + 1} + 3^{2 - x} = 28

x = 2, x = - 1

Solution steps

3^{x + 1} + 3^{2 - x} = 28

Apply exponent rules

3^{x} \cdot 3^{1} + (3^{x})^{- 1} \cdot 3^{2} = 28

Rewrite the equation with

3^{x} = u

u \cdot 3^{1} + (u)^{- 1} \cdot 3^{2} = 28

Solve

u \cdot 3^{1} + u^{- 1} \cdot 3^{2} = 28 : u = 9, u = \frac{1}{3}

u = 9, u = \frac{1}{3}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 9 : x = 2

Solve

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

x = 2, x = - 1

3^{2 x} - 5 (3^{x}) - 36 = 0

83 = 1 5^{x}

50 = \frac{160}{1 + 7 e ^{- 0.3 t}}

4^{x} = 8^{x - 5}

What is the answer to 3^{x+1}+3^{2-x}=28 ?
The answer to 3^{x+1}+3^{2-x}=28 is x=2,x=-1
Solve for x: 3^{x+1}+3^{2-x}=28
The solution is x=2,x=-1