What is the answer to 3^{x+1}-3^{x-1}=72 ?

The answer to 3^{x+1}-3^{x-1}=72 is x=3

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3^{x+1}-3^{x-1}=72

3^{x + 1} - 3^{x - 1} = 72

x = 3

Solution steps

3^{x + 1} - 3^{x - 1} = 72

Factor

3^{x + 1} - 3^{x - 1} : 8 \cdot 3^{x - 1}

8 \cdot 3^{x - 1} = 72

Divide both sides by

8

3^{x - 1} = 9

Apply exponent rules

x - 1 = 2

Solve

x - 1 = 2 : x = 3

x = 3

2^{4^{2 x - 1}} = 4^{2^{x - 1}}

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

5 e^{3 x - 4} = 25

32 \cdot e^{- 0.25 x} = 4

- 14 + 3 e^{x} = 11

What is the answer to 3^{x+1}-3^{x-1}=72 ?
The answer to 3^{x+1}-3^{x-1}=72 is x=3
Solve for x: 3^{x+1}-3^{x-1}=72
The solution is x=3