What is the answer to 3^{2x+1}+3^{x+2}=3 1/3 ?

The answer to 3^{2x+1}+3^{x+2}=3 1/3 is x=-1

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

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

x = - 1

Solution steps

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

Convert mixed numbers to improper fractions:

3 \frac{1}{3} = \frac{10}{3}

3^{2 x + 1} + 3^{x + 2} = \frac{10}{3}

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

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

Solve

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

u = \frac{1}{3}, u = - \frac{10}{3}

Substitute back

u = 3^{x},

solve for

x

Solve

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

Solve

3^{x} = - \frac{10}{3} :

No Solution for

x \in R

x = - 1

8^{x + 1} = 1

9 e^{3 x} = 1

a, 3^{a} + 4^{b} = 5^{c}

4 e^{4 x} = 8

3^{x + 6} = 7

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