What is the answer to 3^{2x-1}=4(3^x)-9 ?

The answer to 3^{2x-1}=4(3^x)-9 is x=2,x=1

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3^{2x-1}=4(3^x)-9

3^{2 x - 1} = 4 (3^{x}) - 9

x = 2, x = 1

Solution steps

3^{2 x - 1} = 4 (3^{x}) - 9

Apply exponent rules

(3^{x})^{2} \cdot 3^{- 1} = 4 \cdot 3^{x} - 9

Rewrite the equation with

3^{x} = u

(u)^{2} \cdot 3^{- 1} = 4 u - 9

Solve

u^{2} \cdot 3^{- 1} = 4 u - 9 : u = 9, u = 3

u = 9, u = 3

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 9 : x = 2

Solve

3^{x} = 3 : x = 1

x = 2, x = 1

2 5^{x + 1} = 5^{- x + 11}

8 (8^{2 x}) - 65 (8^{x}) + 8 = 0

(\frac{1}{25})^{x - 1} = 55

1 = e^{2 x - 3} - 5

What is the answer to 3^{2x-1}=4(3^x)-9 ?
The answer to 3^{2x-1}=4(3^x)-9 is x=2,x=1
Solve for x: 3^{2x-1}=4(3^x)-9
The solution is x=2,x=1