What is the answer to 3^{2x}-3^x-72=0 ?

The answer to 3^{2x}-3^x-72=0 is x=2

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3^{2x}-3^x-72=0

3^{2 x} - 3^{x} - 72 = 0

x = 2

Solution steps

3^{2 x} - 3^{x} - 72 = 0

Apply exponent rules

(3^{x})^{2} - 3^{x} - 72 = 0

Rewrite the equation with

3^{x} = u

(u)^{2} - u - 72 = 0

Solve

u^{2} - u - 72 = 0 : u = 9, u = - 8

u = 9, u = - 8

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 9 : x = 2

Solve

3^{x} = - 8 :

No Solution for

x \in R

x = 2

e^{- 2 k} = 0

2^{3 x} \cdot 7^{x - 1} = 4^{x + 1}

x, (\frac{a}{b})^{x} - 1 = (\frac{b}{a})^{n} - 3

x, 133 1^{x} = (625)^{y}

2^{x} + 2^{x + 2} + 2^{x + 4} = 5370