What is the answer to 5^{2x}-6(5^x)+5=0 ?

The answer to 5^{2x}-6(5^x)+5=0 is x=1,x=0

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5^{2x}-6(5^x)+5=0

5^{2 x} - 6 (5^{x}) + 5 = 0

x = 1, x = 0

Solution steps

5^{2 x} - 6 (5^{x}) + 5 = 0

Apply exponent rules

(5^{x})^{2} - 6 \cdot 5^{x} + 5 = 0

Rewrite the equation with

5^{x} = u

(u)^{2} - 6 u + 5 = 0

Solve

u^{2} - 6 u + 5 = 0 : u = 5, u = 1

u = 5, u = 1

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 5 : x = 1

Solve

5^{x} = 1 : x = 0

x = 1, x = 0

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2^{n} = 1000000

2^{2 x} + 2^{- 2 x} = 23

9^{x} = 12 \cdot 3^{x} - 27

What is the answer to 5^{2x}-6(5^x)+5=0 ?
The answer to 5^{2x}-6(5^x)+5=0 is x=1,x=0
Solve for x: 5^{2x}-6(5^x)+5=0
The solution is x=1,x=0