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

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

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

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

x = - 2

Solution steps

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

Factor

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

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

Divide both sides by

2

3^{x + 2} = 1

Apply exponent rules

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

Solve

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

x = - 2

1^{x} = 2

(4^{x^{2}}) (2^{- 6 x}) = \frac{1}{16}

2^{x} = 16

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

(- 10)^{x} = 1000

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