What is the answer to 9^{x+2}=9^x+240 ?

The answer to 9^{x+2}=9^x+240 is x= 1/2

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9^{x+2}=9^x+240

9^{x + 2} = 9^{x} + 240

x = \frac{1}{2}

Solution steps

9^{x + 2} = 9^{x} + 240

Subtract

9^{x}

from both sides

9^{x + 2} - 9^{x} = 9^{x} + 240 - 9^{x}

Simplify

9^{x + 2} - 9^{x} = 240

Factor

9^{x + 2} - 9^{x} : 80 \cdot 9^{x}

80 \cdot 9^{x} = 240

Divide both sides by

80

9^{x} = 3

Apply exponent rules

2 x = 1

Solve

2 x = 1 : x = \frac{1}{2}

x = \frac{1}{2}

e^{2 - 4 x} = 5

e^{2 - 4 x} = 8

e^{2 - 4 x} = 7

2^{2 x} - 34 \cdot 2^{x} + 64 = 0

3^{2 x + 5} = \frac{1}{27}