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

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

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

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

x = 1, x = - 1

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

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

Solve

u^{2} \cdot 3^{1} = 10 u - 3 : 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

(e^{4 x + 1})^{3} = e^{2}

65 = 1 5^{x}

62 5^{x + 5} = 5^{3 x - 4} 2 5^{2 x - 3}

8 1^{x^{2} - 1} = 27

2^{3 x} = \frac{1}{16}

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