What is the answer to 3^{2x}-2*3^{x+5}+3^{10}=0 ?

The answer to 3^{2x}-2*3^{x+5}+3^{10}=0 is x=5

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3^{2x}-2*3^{x+5}+3^{10}=0

3^{2 x} - 2 \cdot 3^{x + 5} + 3^{10} = 0

x = 5

Solution steps

3^{2 x} - 2 \cdot 3^{x + 5} + 3^{10} = 0

Apply exponent rules

(3^{x})^{2} - 2 \cdot 3^{x} \cdot 3^{5} + 3^{10} = 0

Rewrite the equation with

3^{x} = u

(u)^{2} - 2 u \cdot 3^{5} + 3^{10} = 0

Solve

u^{2} - 2 u \cdot 3^{5} + 3^{10} = 0 : u = 243

u = 243

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 243 : x = 5

x = 5

1 7^{4 - 3 x} = 1

7 = 240 1^{x}

4^{x - 2} = 64

x = e^{\frac{5 x - 6}{3}}

3 2^{- x + 22} = 6 4^{x}

What is the answer to 3^{2x}-2*3^{x+5}+3^{10}=0 ?
The answer to 3^{2x}-2*3^{x+5}+3^{10}=0 is x=5
Solve for x: 3^{2x}-2*3^{x+5}+3^{10}=0
The solution is x=5