What is the answer to 3^{2x}-3^x-6=0 ?

The answer to 3^{2x}-3^x-6=0 is x=1

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3^{2x}-3^x-6=0

3^{2 x} - 3^{x} - 6 = 0

x = 1

Solution steps

3^{2 x} - 3^{x} - 6 = 0

Apply exponent rules

(3^{x})^{2} - 3^{x} - 6 = 0

Rewrite the equation with

3^{x} = u

(u)^{2} - u - 6 = 0

Solve

u^{2} - u - 6 = 0 : u = 3, u = - 2

u = 3, u = - 2

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = 1

Solve

3^{x} = - 2 :

No Solution for

x \in R

x = 1

3^{x} + 3^{x + 2} = 90

1 0^{x} = 31

1 0^{x} = 87

2 5^{3 x + 2} = 125

3^{x} + 5 \cdot 3^{x} = 54