What is the answer to 3^{x+1}-3^x+3^{x-1}=21 ?

The answer to 3^{x+1}-3^x+3^{x-1}=21 is x=2

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3^{x+1}-3^x+3^{x-1}=21

3^{x + 1} - 3^{x} + 3^{x - 1} = 21

x = 2

Solution steps

3^{x + 1} - 3^{x} + 3^{x - 1} = 21

Factor

3^{x + 1} - 3^{x} + 3^{x - 1} : 7 \cdot 3^{x - 1}

7 \cdot 3^{x - 1} = 21

Divide both sides by

7

3^{x - 1} = 3

Apply exponent rules

x - 1 = 1

Solve

x - 1 = 1 : x = 2

x = 2

e^{x - 1} - 1 = 0

\frac{100}{1 + e ^{2 x}} = 1

3^{x} = e^{- 978}

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

4^{x + 2} \times 4^{x} = 120

What is the answer to 3^{x+1}-3^x+3^{x-1}=21 ?
The answer to 3^{x+1}-3^x+3^{x-1}=21 is x=2
Solve for x: 3^{x+1}-3^x+3^{x-1}=21
The solution is x=2