What is the answer to 1=u^{0.1}+u^{0.4}+u^{0.7} ?

The answer to 1=u^{0.1}+u^{0.4}+u^{0.7} is u=0.02549…

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1=u^{0.1}+u^{0.4}+u^{0.7}

1 = u^{0.1} + u^{0.4} + u^{0.7}

u = 0.02549 \dots

Solution steps

1 = u^{0.1} + u^{0.4} + u^{0.7}

Use the following exponent property

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

u^{0.4} = (u^{\frac{1}{10}})^{(0.4 \cdot 10)}, u^{0.7} = (u^{\frac{1}{10}})^{(0.7 \cdot 10)}

1 = u^{\frac{1}{10}} + (u^{\frac{1}{10}})^{4} + (u^{\frac{1}{10}})^{7}

Rewrite the equation with

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

1 = v + v^{4} + v^{7}

Solve

1 = v + v^{4} + v^{7} : v \approx 0.69287 \dots

v \approx 0.69287 \dots

Substitute back

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

solve for

u

Solve

u^{\frac{1}{10}} = 0.69287 \dots : u = 0.02549 \dots

u = 0.02549 \dots

Verify Solutions:

u = 0.02549 \dots

True

The solution is

u = 0.02549 \dots

- x - x^{2} - 2 x = 0

4 + 21 e^{- 0.2} = 8

100 = 53 Q^{0.18}

(x + 3)^{\frac{2}{3}} = 25

\frac{- 1}{- x ^{2} + 2 x} = - 2

What is the answer to 1=u^{0.1}+u^{0.4}+u^{0.7} ?
The answer to 1=u^{0.1}+u^{0.4}+u^{0.7} is u=0.02549…
Solve for u: 1=u^{0.1}+u^{0.4}+u^{0.7}
The solution is u=0.02549…