What is the answer to 25(5^{2x})-626(5^x)+25=0 ?

The answer to 25(5^{2x})-626(5^x)+25=0 is x=2,x=-2

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25(5^{2x})-626(5^x)+25=0

25 (5^{2 x}) - 626 (5^{x}) + 25 = 0

x = 2, x = - 2

Solution steps

25 (5^{2 x}) - 626 (5^{x}) + 25 = 0

Apply exponent rules

25 (5^{x})^{2} - 626 \cdot 5^{x} + 25 = 0

Rewrite the equation with

5^{x} = u

25 (u)^{2} - 626 u + 25 = 0

Solve

25 u^{2} - 626 u + 25 = 0 : u = 25, u = \frac{1}{25}

u = 25, u = \frac{1}{25}

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 25 : x = 2

Solve

5^{x} = \frac{1}{25} : x = - 2

x = 2, x = - 2

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

5 e^{3 t} = 8 e^{2 t}

125 = (\frac{1}{25})^{y - 1}

3 e^{2 x} + 5 = 16 e^{x}

450000 = 200000 (1 + 0.16)^{x}

What is the answer to 25(5^{2x})-626(5^x)+25=0 ?
The answer to 25(5^{2x})-626(5^x)+25=0 is x=2,x=-2
Solve for x: 25(5^{2x})-626(5^x)+25=0
The solution is x=2,x=-2