What is the answer to 27^x-9^{x+0.5}-3^x+3=0 ?

The answer to 27^x-9^{x+0.5}-3^x+3=0 is x=1,x=0

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27^x-9^{x+0.5}-3^x+3=0

2 7^{x} - 9^{x + 0.5} - 3^{x} + 3 = 0

x = 1, x = 0

Solution steps

2 7^{x} - 9^{x + 0.5} - 3^{x} + 3 = 0

Apply exponent rules

(3^{x})^{3} - (3^{x})^{2} \cdot 3^{1} - 3^{x} + 3 = 0

Rewrite the equation with

3^{x} = u

(u)^{3} - (u)^{2} \cdot 3^{1} - u + 3 = 0

Solve

u^{3} - u^{2} \cdot 3^{1} - u + 3 = 0 : u = 3, u = - 1, u = 1

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

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = 1

Solve

3^{x} = - 1 :

No Solution for

x \in R

Solve

3^{x} = 1 : x = 0

x = 1, x = 0

2. 5^{2 - 3 x} = 0.1 6^{2 x}

x^{5} = 9^{x}

6 e^{x} - 4 e^{- x} = 5

T, x^{T} A^{T} A x = 0

e^{4 x} = 8 e^{x}

What is the answer to 27^x-9^{x+0.5}-3^x+3=0 ?
The answer to 27^x-9^{x+0.5}-3^x+3=0 is x=1,x=0
Solve for x: 27^x-9^{x+0.5}-3^x+3=0
The solution is x=1,x=0