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

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

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

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

x = 2

Solution steps

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

Apply exponent rules

3^{x} \cdot 3^{1} + (3^{x})^{2} = 108

Rewrite the equation with

3^{x} = u

u \cdot 3^{1} + (u)^{2} = 108

Solve

u \cdot 3^{1} + u^{2} = 108 : u = 9, u = - 12

u = 9, u = - 12

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 9 : x = 2

Solve

3^{x} = - 12 :

No Solution for

x \in R

x = 2

3^{7 x + 4} = (\frac{1}{27})^{x - 3}

e^{4 - 4 x} = 5

1 0^{x + 8} = 36

x, e^{x} (y - 2) = y

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