What is the answer to 3^{2x+1}=28(3^x)-9 ?

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

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3^{2x+1}=28(3^x)-9

3^{2 x + 1} = 28 (3^{x}) - 9

x = 2, x = - 1

Solution steps

3^{2 x + 1} = 28 (3^{x}) - 9

Apply exponent rules

(3^{x})^{2} \cdot 3^{1} = 28 \cdot 3^{x} - 9

Rewrite the equation with

3^{x} = u

(u)^{2} \cdot 3^{1} = 28 u - 9

Solve

u^{2} \cdot 3^{1} = 28 u - 9 : 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

30 = 6 ln (1.8) (1. 8^{x})

(\frac{4}{5})^{\frac{1}{x}} = 3

e^{2 x} + 2 e^{x} - 15 = 0

4^{x} = 4^{5}

3^{x} \cdot 5^{x - 1} = 10125

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