What is the answer to 27^x-3^{x+2}=9^x-9 ?

The answer to 27^x-3^{x+2}=9^x-9 is x=0,x=1

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27^x-3^{x+2}=9^x-9

2 7^{x} - 3^{x + 2} = 9^{x} - 9

x = 0, x = 1

Solution steps

2 7^{x} - 3^{x + 2} = 9^{x} - 9

Apply exponent rules

(3^{x})^{3} - 3^{x} \cdot 3^{2} = (3^{x})^{2} - 9

Rewrite the equation with

3^{x} = u

(u)^{3} - u \cdot 3^{2} = (u)^{2} - 9

Solve

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

u = 1, u = - 3, u = 3

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 1 : x = 0

Solve

3^{x} = - 3 :

No Solution for

x \in R

Solve

3^{x} = 3 : x = 1

x = 0, x = 1

1 0^{x + 2} - 1 0^{x} = 9900

2 e^{2 x} + 2 e^{- 2 x} - e^{x} + e^{- x} = 7

1 0^{x + 8} = 6^{2 x}

34.416 e^{- 0.18 t} = 6

(16 + \frac{0.878}{26})^{3 t} = 30

What is the answer to 27^x-3^{x+2}=9^x-9 ?
The answer to 27^x-3^{x+2}=9^x-9 is x=0,x=1
Solve for x: 27^x-3^{x+2}=9^x-9
The solution is x=0,x=1