What is the answer to 9^x-7*3^x=18 ?

The answer to 9^x-7*3^x=18 is x=2

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9^x-7*3^x=18

9^{x} - 7 \cdot 3^{x} = 18

x = 2

Solution steps

9^{x} - 7 \cdot 3^{x} = 18

Apply exponent rules

(3^{x})^{2} - 7 \cdot 3^{x} = 18

Rewrite the equation with

3^{x} = u

(u)^{2} - 7 u = 18

Solve

u^{2} - 7 u = 18 : u = 9, u = - 2

u = 9, u = - 2

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 9 : x = 2

Solve

3^{x} = - 2 :

No Solution for

x \in R

x = 2

128 = 2^{n - 1}

8 + 3 e^{3 + x} = 10

7^{3 x + 2} = 21

7^{3 x + 2} = 28

7^{3 x + 2} = 35