What is the answer to 7^x+7^{x+2}=-2051+7^{x+3} ?

The answer to 7^x+7^{x+2}=-2051+7^{x+3} is x=1

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7^x+7^{x+2}=-2051+7^{x+3}

7^{x} + 7^{x + 2} = - 2051 + 7^{x + 3}

x = 1

Solution steps

7^{x} + 7^{x + 2} = - 2051 + 7^{x + 3}

Subtract

7^{x + 3}

from both sides

7^{x} + 7^{x + 2} - 7^{x + 3} = - 2051 + 7^{x + 3} - 7^{x + 3}

Simplify

7^{x} + 7^{x + 2} - 7^{x + 3} = - 2051

Factor

7^{x} + 7^{x + 2} - 7^{x + 3} : - 293 \cdot 7^{x}

- 293 \cdot 7^{x} = - 2051

Divide both sides by

- 293

7^{x} = 7

Apply exponent rules

x = 1

2 7^{x} (9^{2 x - 1}) = 3^{x + 4}

2^{8 x + 3} = 2

\frac{27}{9 ^{x}} = 3^{x - 1}

3 6^{2 x - 7} = 6^{x - 5}

3^{x + 1} - 2 = 25

What is the answer to 7^x+7^{x+2}=-2051+7^{x+3} ?
The answer to 7^x+7^{x+2}=-2051+7^{x+3} is x=1
Solve for x: 7^x+7^{x+2}=-2051+7^{x+3}
The solution is x=1