What is the answer to x^{0.16}-x^{0.15}=5000 ?

The answer to x^{0.16}-x^{0.15}=5000 is x=10.31317…^{25}

Solve for x: x^{0.16}-x^{0.15}=5000

The solution is x=10.31317…^{25}

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x^{0.16} - x^{0.15} = 5000

x = 10.31317 \dots^{25}

Decimal Notation

x = 2.16179 E 25

Solution steps

x^{0.16} - x^{0.15} = 5000

Use the following exponent property

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

x^{0.16} = (x^{\frac{1}{25}})^{(0.16 \cdot 25)}, x^{0.15} = (x^{\frac{1}{25}})^{(0.15 \cdot 25)}

(x^{\frac{1}{25}})^{4} - (x^{\frac{1}{25}})^{\frac{15}{4}} = 5000

Rewrite the equation with

x^{\frac{1}{25}} = u

u^{4} - u^{\frac{15}{4}} = 5000

Solve

u^{4} - u^{\frac{15}{4}} = 5000 : u = 10.31317 \dots

u = 10.31317 \dots

Substitute back

u = x^{\frac{1}{25}},

solve for

x

Solve

x^{\frac{1}{25}} = 10.31317 \dots : x = 10.31317 \dots^{25}

x = 10.31317 \dots^{25}

Verify Solutions:

x = 10.31317 \dots^{25}

True

The solution is

x = 10.31317 \dots^{25}

x = x^{2} - 4

2 x + 6 = 2

2 x + 6 = 0

5 = r - 3

\frac{- 1 + 4 y + 9}{2} = 0

What is the answer to x^{0.16}-x^{0.15}=5000 ?
The answer to x^{0.16}-x^{0.15}=5000 is x=10.31317…^{25}
Solve for x: x^{0.16}-x^{0.15}=5000
The solution is x=10.31317…^{25}