What is the answer to x^{0.3}x=6x-2 ?

The answer to x^{0.3}x=6x-2 is x=0.38084…,x=391.38488…

Solve for x: x^{0.3}x=6x-2

The solution is x=0.38084…,x=391.38488…

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x^{0.3} x = 6 x - 2

x = 0.38084 \dots, x = 391.38488 \dots

Solution steps

x^{0.3} x = 6 x - 2

Use the following exponent property

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

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

(x^{\frac{1}{10}})^{3} (x^{\frac{1}{10}})^{10} = 6 (x^{\frac{1}{10}})^{10} - 2

Rewrite the equation with

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

u^{3} u^{10} = 6 u^{10} - 2

Solve

u^{3} u^{10} = 6 u^{10} - 2 : u \approx - 0.88617 \dots, u \approx 0.90797 \dots, u \approx 1.81660 \dots

u \approx - 0.88617 \dots, u \approx 0.90797 \dots, u \approx 1.81660 \dots

Substitute back

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

solve for

x

Solve

x^{\frac{1}{10}} = - 0.88617 \dots :

No Solution for

x \in R

Solve

x^{\frac{1}{10}} = 0.90797 \dots : x = 0.38084 \dots

Solve

x^{\frac{1}{10}} = 1.81660 \dots : x = 391.38488 \dots

x = 0.38084 \dots, x = 391.38488 \dots

Verify Solutions:

x = 0.38084 \dots

True

, x = 391.38488 \dots

True

The solutions are

x = 0.38084 \dots, x = 391.38488 \dots

4 a^{2} - 4 a + 1 + [a + 4] = a + 7

11 - x = x - 5

5 x + 6 + 7 = 3

2 x + 5 + 3 x - 14 = 9

What is the answer to x^{0.3}x=6x-2 ?
The answer to x^{0.3}x=6x-2 is x=0.38084…,x=391.38488…
Solve for x: x^{0.3}x=6x-2
The solution is x=0.38084…,x=391.38488…