What is the answer to 5^{6x}-6(125^x)+5=0 ?

The answer to 5^{6x}-6(125^x)+5=0 is x= 1/3 ,x=0

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5^{6x}-6(125^x)+5=0

5^{6 x} - 6 (12 5^{x}) + 5 = 0

x = \frac{1}{3}, x = 0

Solution steps

5^{6 x} - 6 (12 5^{x}) + 5 = 0

Apply exponent rules

(5^{x})^{6} - 6 (5^{x})^{3} + 5 = 0

Rewrite the equation with

5^{x} = u

(u)^{6} - 6 (u)^{3} + 5 = 0

Solve

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 1 : x = 0

x = \frac{1}{3}, x = 0

4 \cdot 2^{x} = 2^{6 x + 3}

9^{2 - x} = (\frac{1}{3})^{2 x + 1}

(\frac{1}{4})^{x} = 4

(2)^{k} = 0.25

3^{2 x} - 10 (3^{x}) + 9 = 0

What is the answer to 5^{6x}-6(125^x)+5=0 ?
The answer to 5^{6x}-6(125^x)+5=0 is x= 1/3 ,x=0
Solve for x: 5^{6x}-6(125^x)+5=0
The solution is x= 1/3 ,x=0