What is the answer to 2n^2log_{2}(n)=n^3 ?

The answer to 2n^2log_{2}(n)=n^3 is n=4,n=2

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2n^2log_{2}(n)=n^3

2 n^{2} lo g_{2} (n) = n^{3}

n = 4, n = 2

Solution steps

2 n^{2} lo g_{2} (n) = n^{3}

Move

n^{3}

to the left side

2 n^{2} lo g_{2} (n) - n^{3} = 0

Factor

2 n^{2} lo g_{2} (n) - n^{3} : n^{2} (2 lo g_{2} (n) - n)

n^{2} (2 lo g_{2} (n) - n) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

n = 0 or 2 lo g_{2} (n) - n = 0

Solve

2 lo g_{2} (n) - n = 0 : n = 4, n = 2

Verify Solutions:

n = 0

False

, n = 4

True

, n = 2

True

The solutions are

n = 4, n = 2

20 lo g_{10} (x) = - 40

lo g_{5} (5 x - 5) = 3

y, - ln (y) = ln (x)

- 3.01 = 20 lo g_{10} (K)

3 lo g_{9} (5 x - 5) = 5

What is the answer to 2n^2log_{2}(n)=n^3 ?
The answer to 2n^2log_{2}(n)=n^3 is n=4,n=2
Solve for n: 2n^2log_{2}(n)=n^3
The solution is n=4,n=2