What is the answer to 9(3^{2x})-28(3^x)+3=0 ?

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

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9(3^{2x})-28(3^x)+3=0

9 (3^{2 x}) - 28 (3^{x}) + 3 = 0

x = 1, x = - 2

Solution steps

9 (3^{2 x}) - 28 (3^{x}) + 3 = 0

Apply exponent rules

9 (3^{x})^{2} - 28 \cdot 3^{x} + 3 = 0

Rewrite the equation with

3^{x} = u

9 (u)^{2} - 28 u + 3 = 0

Solve

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

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

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = 1

Solve

3^{x} = \frac{1}{9} : x = - 2

x = 1, x = - 2

(\frac{1}{3})^{2 x + 3} = 5

8 + 0.04 x = 6 (1.02)^{x}

x^{10} = e^{x}

4^{x} = \frac{8}{1 6 ^{x}}

x, e^{x} = 4

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