What is the answer to 25^x-6*5^x+5=0 ?

The answer to 25^x-6*5^x+5=0 is x=1,x=0

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25^x-6*5^x+5=0

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

x = 1, x = 0

Solution steps

2 5^{x} - 6 \cdot 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

2^{x + 1} = 8

3^{x} = 17

x, y = e^{x}

(\frac{2}{3})^{x} = 5^{1 - x}

3 e^{x} + 5 = 8