What is the answer to 3^{2x+1}-10*3^x+3=0 ?

The answer to 3^{2x+1}-10*3^x+3=0 is x=1,x=-1

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3^{2x+1}-10*3^x+3=0

3^{2 x + 1} - 10 \cdot 3^{x} + 3 = 0

x = 1, x = - 1

Solution steps

3^{2 x + 1} - 10 \cdot 3^{x} + 3 = 0

Apply exponent rules

(3^{x})^{2} \cdot 3^{1} - 10 \cdot 3^{x} + 3 = 0

Rewrite the equation with

3^{x} = u

(u)^{2} \cdot 3^{1} - 10 u + 3 = 0

Solve

u^{2} \cdot 3^{1} - 10 u + 3 = 0 : u = 3, u = \frac{1}{3}

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

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = 1

Solve

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

x = 1, x = - 1

5^{4 x - 2} = 2 5^{x + 1}

4^{(x + 3)} - 4^{(x + 2)} = 24

3^{x + 3} = 27

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

3^{x} e^{7 x + 2} = 15

What is the answer to 3^{2x+1}-10*3^x+3=0 ?
The answer to 3^{2x+1}-10*3^x+3=0 is x=1,x=-1
Solve for x: 3^{2x+1}-10*3^x+3=0
The solution is x=1,x=-1