What is the answer to 3^{x+2}+9^{x+1}=108 ?

The answer to 3^{x+2}+9^{x+1}=108 is x=1

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3^{x+2}+9^{x+1}=108

3^{x + 2} + 9^{x + 1} = 108

x = 1

Solution steps

3^{x + 2} + 9^{x + 1} = 108

Apply exponent rules

3^{x} \cdot 3^{2} + (3^{x})^{2} \cdot 3^{2} = 108

Rewrite the equation with

3^{x} = u

u \cdot 3^{2} + (u)^{2} \cdot 3^{2} = 108

Solve

u \cdot 3^{2} + u^{2} \cdot 3^{2} = 108 : u = 3, u = - 4

u = 3, u = - 4

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = 1

Solve

3^{x} = - 4 :

No Solution for

x \in R

x = 1

130 = 52 e^{k \cdot 20}

x, y^{2} = 153 + 2^{x}

y, x = 3 - e^{2 y}

1 6^{x} = \frac{1}{4}

x, z = ln (e^{x} + e^{y})

What is the answer to 3^{x+2}+9^{x+1}=108 ?
The answer to 3^{x+2}+9^{x+1}=108 is x=1
Solve for x: 3^{x+2}+9^{x+1}=108
The solution is x=1