What is the answer to 3^{2x}-3^{x-1}=3^{x+1}-1 ?

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

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3^{2x}-3^{x-1}=3^{x+1}-1

3^{2 x} - 3^{x - 1} = 3^{x + 1} - 1

x = 1, x = - 1

Solution steps

3^{2 x} - 3^{x - 1} = 3^{x + 1} - 1

Apply exponent rules

(3^{x})^{2} - 3^{x} \cdot 3^{- 1} = 3^{x} \cdot 3^{1} - 1

Rewrite the equation with

3^{x} = u

(u)^{2} - u \cdot 3^{- 1} = u \cdot 3^{1} - 1

Solve

u^{2} - u \cdot 3^{- 1} = u \cdot 3^{1} - 1 : u = 3, u = \frac{1}{3}

u = 3, u = \frac{1}{3}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = 1

Solve

3^{x} = \frac{1}{3} : x = - 1

x = 1, x = - 1

3^{2 x - 7} = 27

2^{x^{3}} = 3 2^{x}

2 \cdot 3^{x} = 7 \cdot 5^{x}

129 6^{3 x - 3} = 21 6^{3 x - 5}

2 0^{- 2 x + 3} = 4^{3 x - 1} \cdot 5^{- x + 4}

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