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

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

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

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

x = 1, x = 0

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

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

Solve

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

y, e^{- e^{- y}} = 1 - 0.05

e^{2 x} - 9 e^{x} + 8 = 0

e^{x} = x e^{x}

e^{x} = 11

e^{x} = 34

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