What is the answer to 3^x+3^{x+3}-3^{x-1}=249 ?

The answer to 3^x+3^{x+3}-3^{x-1}=249 is x=2

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3^x+3^{x+3}-3^{x-1}=249

3^{x} + 3^{x + 3} - 3^{x - 1} = 249

x = 2

Solution steps

3^{x} + 3^{x + 3} - 3^{x - 1} = 249

Factor

3^{x} + 3^{x + 3} - 3^{x - 1} : 83 \cdot 3^{x - 1}

83 \cdot 3^{x - 1} = 249

Divide both sides by

83

3^{x - 1} = 3

Apply exponent rules

x - 1 = 1

Solve

x - 1 = 1 : x = 2

x = 2

5 \cdot 2^{x} = 2 \cdot 4^{x} + 2

2^{3 - 2 x} = 32

lo g_{3} (2^{x} + 1) = 2

1 = (3)^{x}

[4^{x + 1}] - (4^{x}) = 48

What is the answer to 3^x+3^{x+3}-3^{x-1}=249 ?
The answer to 3^x+3^{x+3}-3^{x-1}=249 is x=2
Solve for x: 3^x+3^{x+3}-3^{x-1}=249
The solution is x=2