What is the answer to 9^x-28*3^{x-1}+3=0 ?

The answer to 9^x-28*3^{x-1}+3=0 is x=2,x=-1

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9^x-28*3^{x-1}+3=0

9^{x} - 28 \cdot 3^{x - 1} + 3 = 0

x = 2, x = - 1

Solution steps

9^{x} - 28 \cdot 3^{x - 1} + 3 = 0

Apply exponent rules

(3^{x})^{2} - 28 \cdot 3^{x} \cdot 3^{- 1} + 3 = 0

Rewrite the equation with

3^{x} = u

(u)^{2} - 28 u \cdot 3^{- 1} + 3 = 0

Solve

u^{2} - 28 u \cdot 3^{- 1} + 3 = 0 : u = 9, u = \frac{1}{3}

u = 9, u = \frac{1}{3}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 9 : x = 2

Solve

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

x = 2, x = - 1

9^{k - 2} \cdot 81 = 9^{2 k}

e^{2 x} - e^{x} = 20

y, x = 4 + y + e^{y}

1 6^{n} = 4^{3}

\frac{1}{5 ^{3}} = 5^{p}

What is the answer to 9^x-28*3^{x-1}+3=0 ?
The answer to 9^x-28*3^{x-1}+3=0 is x=2,x=-1
Solve for x: 9^x-28*3^{x-1}+3=0
The solution is x=2,x=-1