What is the answer to 0.2x^{0.7}=0.2x^{0.1} ?

The answer to 0.2x^{0.7}=0.2x^{0.1} is x=0,x=1

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0.2x^{0.7}=0.2x^{0.1}

0.2 x^{0.7} = 0.2 x^{0.1}

x = 0, x = 1

Solution steps

0.2 x^{0.7} = 0.2 x^{0.1}

Move

0.2 x^{0.1}

to the left side

0.2 x^{0.7} - 0.2 x^{0.1} = 0

Factor

0.2 x^{0.7} - 0.2 x^{0.1} : 0.2 x^{0.1} (x^{0.6} - 1)

0.2 x^{0.1} (x^{0.6} - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x^{0.1} = 0 or x^{0.6} - 1 = 0

Solve

x^{0.1} = 0 : x = 0

Solve

x^{0.6} - 1 = 0 : x = 1

x = 0, x = 1

Verify Solutions:

x = 0

True

, x = 1

True

The solutions are

x = 0, x = 1

x + 6 = x + 6

- 3 x (2 - x^{2})^{\frac{1}{2}} = 0

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

What is the answer to 0.2x^{0.7}=0.2x^{0.1} ?
The answer to 0.2x^{0.7}=0.2x^{0.1} is x=0,x=1
Solve for x: 0.2x^{0.7}=0.2x^{0.1}
The solution is x=0,x=1