What is the answer to 3^{x+2}+3^x+3^{x-2}=91 ?

The answer to 3^{x+2}+3^x+3^{x-2}=91 is x=2

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3^{x+2}+3^x+3^{x-2}=91

3^{x + 2} + 3^{x} + 3^{x - 2} = 91

x = 2

Solution steps

3^{x + 2} + 3^{x} + 3^{x - 2} = 91

Factor

3^{x + 2} + 3^{x} + 3^{x - 2} : 91 \cdot 3^{x - 2}

91 \cdot 3^{x - 2} = 91

Divide both sides by

91

3^{x - 2} = 1

Apply exponent rules

(x - 2) ln (3) = ln (1)

Solve

(x - 2) ln (3) = ln (1) : x = 2

x = 2

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

3^{2 x} - 30 (3^{x}) + 81 = 0

x, e^{x} = e^{y}

8^{3 - x} = 4 \cdot 2^{1 - 2 x}

\frac{1}{49} = 7^{n}

What is the answer to 3^{x+2}+3^x+3^{x-2}=91 ?
The answer to 3^{x+2}+3^x+3^{x-2}=91 is x=2
Solve for x: 3^{x+2}+3^x+3^{x-2}=91
The solution is x=2