What is the answer to n^{3.2}=(4n)/(2.5) ?

The answer to n^{3.2}=(4n)/(2.5) is n=0,n=1.23817…

Solve for n: n^{3.2}=(4n)/(2.5)

The solution is n=0,n=1.23817…

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n^{3.2} = \frac{4 n}{2.5}

n = 0, n = 1.23817 \dots

Solution steps

n^{3.2} = \frac{4 n}{2.5}

Multiply both sides by

2.5

n^{3.2} \cdot 2.5 = \frac{4 n}{2.5} \cdot 2.5

Simplify

n^{3.2} \cdot 2.5 = 4 n

Use the following exponent property

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

n^{3.2} = (n^{\frac{1}{5}})^{(3.2 \cdot 5)}

(n^{\frac{1}{5}})^{16} \cdot 2.5 = 4 (n^{\frac{1}{5}})^{5}

Rewrite the equation with

n^{\frac{1}{5}} = u

u^{16} \cdot 2.5 = 4 u^{5}

Solve

u^{16} \cdot 2.5 = 4 u^{5} : u = 0, u = 1.04365 \dots

u = 0, u = 1.04365 \dots

Substitute back

u = n^{\frac{1}{5}},

solve for

n

Solve

n^{\frac{1}{5}} = 0 : n = 0

Solve

n^{\frac{1}{5}} = 1.04365 \dots : n = 1.23817 \dots

n = 0, n = 1.23817 \dots

Verify Solutions:

n = 0

True

, n = 1.23817 \dots

True

The solutions are

n = 0, n = 1.23817 \dots

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

5 x + 9 = 7

x, y = 1 - x

x^{0.7} = 0.4 \cdot 10 0^{0.7}

5 = 6 x + 1 - 2

What is the answer to n^{3.2}=(4n)/(2.5) ?
The answer to n^{3.2}=(4n)/(2.5) is n=0,n=1.23817…
Solve for n: n^{3.2}=(4n)/(2.5)
The solution is n=0,n=1.23817…