What is the answer to 4*3^{x-1}-1=3^{2x-1} ?

The answer to 4*3^{x-1}-1=3^{2x-1} is x=1,x=0

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4*3^{x-1}-1=3^{2x-1}

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

x = 1, x = 0

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

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

Solve

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

u = 3, u = 1

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = 1

Solve

3^{x} = 1 : x = 0

x = 1, x = 0

x e^{x} + e^{x} = 0

e^{2 x} - 7 e^{x} + 6 = 0

3^{2 x + 1} = 9^{x - 2}

10 = 2^{x}

3 6^{(3 x - 1)} = 6^{(4 x + 2)}

What is the answer to 4*3^{x-1}-1=3^{2x-1} ?
The answer to 4*3^{x-1}-1=3^{2x-1} is x=1,x=0
Solve for x: 4*3^{x-1}-1=3^{2x-1}
The solution is x=1,x=0