What is the answer to x^{0.3}x-82=x-6 ?

The answer to x^{0.3}x-82=x-6 is x=38.28974…

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x^{0.3}x-82=x-6

x^{0.3} x - 82 = x - 6

x = 38.28974 \dots

Solution steps

x^{0.3} x - 82 = x - 6

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

Rewrite the equation with

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

u^{3} u^{10} - 82 = u^{10} - 6

Solve

u^{3} u^{10} - 82 = u^{10} - 6 : u \approx 1.43982 \dots

u \approx 1.43982 \dots

Substitute back

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

solve for

x

Solve

x^{\frac{1}{10}} = 1.43982 \dots : x = 38.28974 \dots

x = 38.28974 \dots

Verify Solutions:

x = 38.28974 \dots

True

The solution is

x = 38.28974 \dots

1 = x x

x + 67 = x + 11

7 x - 3 = x + 1

x - 11 x + 24 = 0

What is the answer to x^{0.3}x-82=x-6 ?
The answer to x^{0.3}x-82=x-6 is x=38.28974…
Solve for x: x^{0.3}x-82=x-6
The solution is x=38.28974…