What is the answer to 9^{x+1}+3=28\times 3^x ?

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

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9^{x+1}+3=28\times 3^x

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

x = 1, x = - 2

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

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

Solve

u^{2} \cdot 3^{2} + 3 = 28 u : 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

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

e^{2 x} + 9 - e^{2 x} - 4 = 1

\frac{e ^{4 x + 7}}{3} + 1 = 12

3 \cdot 9^{x} \cdot 2 7^{x} = 1

3^{3 x - 4} = 24 3^{x}

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