What is the answer to y^{0.3}(2y+4)=8y ?

The answer to y^{0.3}(2y+4)=8y is y=0,y=94.76130…,y=0.51551…

Solve for y: y^{0.3}(2y+4)=8y

The solution is y=0,y=94.76130…,y=0.51551…

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y^{0.3} (2 y + 4) = 8 y

y = 0, y = 94.76130 \dots, y = 0.51551 \dots

Solution steps

y^{0.3} (2 y + 4) = 8 y

Use the following exponent property

: a^{n} = (a^{\frac{1}{m}})^{(n \cdot m)}

y^{0.3} = (y^{\frac{1}{10}})^{(0.3 \cdot 10)}

(y^{\frac{1}{10}})^{3} (2 (y^{\frac{1}{10}})^{10} + 4) = 8 (y^{\frac{1}{10}})^{10}

Rewrite the equation with

y^{\frac{1}{10}} = u

u^{3} (2 u^{10} + 4) = 8 u^{10}

Solve

u^{3} (2 u^{10} + 4) = 8 u^{10} : u = 0, u \approx 1.57638 \dots, u \approx 0.93588 \dots

u = 0, u \approx 1.57638 \dots, u \approx 0.93588 \dots

Substitute back

u = y^{\frac{1}{10}},

solve for

y

Solve

y^{\frac{1}{10}} = 0 : y = 0

Solve

y^{\frac{1}{10}} = 1.57638 \dots : y = 94.76130 \dots

Solve

y^{\frac{1}{10}} = 0.93588 \dots : y = 0.51551 \dots

y = 0, y = 94.76130 \dots, y = 0.51551 \dots

Verify Solutions:

y = 0

True

, y = 94.76130 \dots

True

, y = 0.51551 \dots

True

The solutions are

y = 0, y = 94.76130 \dots, y = 0.51551 \dots

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

7 x + 16 = 9 x - 8

x^{\frac{1}{2}} = 64

x, - f = x^{2} - x

u = 9 u - 14

What is the answer to y^{0.3}(2y+4)=8y ?
The answer to y^{0.3}(2y+4)=8y is y=0,y=94.76130…,y=0.51551…
Solve for y: y^{0.3}(2y+4)=8y
The solution is y=0,y=94.76130…,y=0.51551…