What is the answer to 25000+x^{0.16}=30000+x^{0.15} ?

The answer to 25000+x^{0.16}=30000+x^{0.15} is x=10.31317…^{25}

Solve for x: 25000+x^{0.16}=30000+x^{0.15}

The solution is x=10.31317…^{25}

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25000 + x^{0.16} = 30000 + x^{0.15}

x = 10.31317 \dots^{25}

Decimal Notation

x = 2.16179 E 25

Solution steps

25000 + x^{0.16} = 30000 + x^{0.15}

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)}

25000 + (x^{\frac{1}{25}})^{4} = 30000 + (x^{\frac{1}{25}})^{\frac{15}{4}}

Rewrite the equation with

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

25000 + u^{4} = 30000 + u^{\frac{15}{4}}

Solve

25000 + u^{4} = 30000 + u^{\frac{15}{4}} : 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 + 11 + x = 1

x^{\frac{3}{7}} = 27

4 x + 5 = 3 + 2 x - 6

x, 2 x - 7 = 1

a, b = 1 - a^{2}

What is the answer to 25000+x^{0.16}=30000+x^{0.15} ?
The answer to 25000+x^{0.16}=30000+x^{0.15} is x=10.31317…^{25}
Solve for x: 25000+x^{0.16}=30000+x^{0.15}
The solution is x=10.31317…^{25}