What is the answer to 316=240*N^{-0.135135} ?

The answer to 316=240*N^{-0.135135} is No Solution for N\in\mathbb{R}

Solve for N: 316=240*N^{-0.135135}

The solution is No Solution for N\in\mathbb{R}

316 = 240 \cdot N^{- 0.135135}

No Solution for N \in R

Solution steps

316 = 240 N^{- 0.135135}

Expand

240 N^{- 0.135135} : \frac{240}{N ^{0.135135}}

316 = \frac{240}{N ^{0.135135}}

Take both sides of the equation to the power of

37 : 31 6^{37} = \frac{24 0 ^{37}}{N ^{4.999995}}

31 6^{37} = \frac{24 0 ^{37}}{N ^{4.999995}}

Use the following exponent property

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

N^{4.999995} = (N^{\frac{1}{1}})^{(4.999995 \cdot 1)}

31 6^{37} = \frac{24 0 ^{37}}{( N ^{\frac{1}{1}} ) ^{5}}

Rewrite the equation with

N^{\frac{1}{1}} = u

31 6^{37} = \frac{24 0 ^{37}}{u ^{5}}

Solve

31 6^{37} = \frac{24 0 ^{37}}{u ^{5}} : u = \frac{2799360000000 5 3600}{7 9 ^{7} 5 6241}

u = \frac{2799360000000 5 3600}{7 9 ^{7} 5 6241}

Substitute back

u = N^{\frac{1}{1}},

solve for

N

Solve

N^{\frac{1}{1}} = \frac{2799360000000 5 3600}{7 9 ^{7} 5 6241} : N = \frac{2799360000000 5 3600}{7 9 ^{7} 5 6241}

N = \frac{2799360000000 5 3600}{7 9 ^{7} 5 6241}

Verify Solutions:

N = \frac{2799360000000 5 3600}{7 9 ^{7} 5 6241}

False

The solution is

No Solution for N \in R

x + 105 = x + 15

143 + 26 z - z = 12

5 x + 10 = 2 x - 1

26 = y^{0.8}

3 x^{\frac{2}{3}} - 30 = 18

What is the answer to 316=240*N^{-0.135135} ?
The answer to 316=240*N^{-0.135135} is No Solution for N\in\mathbb{R}
Solve for N: 316=240*N^{-0.135135}
The solution is No Solution for N\in\mathbb{R}