What is the answer to 25(5^{2x})-126(5^x)+5=0 ?

The answer to 25(5^{2x})-126(5^x)+5=0 is x=1,x=-2

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25(5^{2x})-126(5^x)+5=0

25 (5^{2 x}) - 126 (5^{x}) + 5 = 0

x = 1, x = - 2

Solution steps

25 (5^{2 x}) - 126 (5^{x}) + 5 = 0

Apply exponent rules

25 (5^{x})^{2} - 126 \cdot 5^{x} + 5 = 0

Rewrite the equation with

5^{x} = u

25 (u)^{2} - 126 u + 5 = 0

Solve

25 u^{2} - 126 u + 5 = 0 : u = 5, u = \frac{1}{25}

u = 5, u = \frac{1}{25}

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 5 : x = 1

Solve

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

x = 1, x = - 2

5^{x} - 5^{- x} = 2

2^{3 x + 2} = 8

lo g_{7} (2^{4 + 3 x}) = 10

- 5 \cdot e^{10 t} = - 30

y, x^{y} = 3

What is the answer to 25(5^{2x})-126(5^x)+5=0 ?
The answer to 25(5^{2x})-126(5^x)+5=0 is x=1,x=-2
Solve for x: 25(5^{2x})-126(5^x)+5=0
The solution is x=1,x=-2