What is the answer to 1n^2=2nlog_{10}(n) ?

The answer to 1n^2=2nlog_{10}(n) is No Solution for n\in\mathbb{R}

Solve for n: 1n^2=2nlog_{10}(n)

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

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1 n^{2} = 2 n lo g_{10} (n)

No Solution for n \in R

Solution steps

1 \cdot n^{2} = 2 n lo g_{10} (n)

Switch sides

2 n lo g_{10} (n) = 1 \cdot n^{2}

Multiply:

1 \cdot n^{2} = n^{2}

2 n lo g_{10} (n) = n^{2}

Move

n^{2}

to the left side

2 n lo g_{10} (n) - n^{2} = 0

Factor

2 n lo g_{10} (n) - n^{2} : n (2 lo g_{10} (n) - n)

n (2 lo g_{10} (n) - n) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

n = 0 or 2 lo g_{10} (n) - n = 0

Solve

2 lo g_{10} (n) - n = 0 :

No Solution for

n \in R

Verify Solutions:

n = 0

False

The solution is

No Solution for n \in R

lo g_{b} (4) = 3

lo g_{2} (8 x + 3) = 5

lo g_{2} (5 x) - lo g_{2} (2) = 3

x, 4 ln (3 x) = 16

- 2 x + 5 \cdot ln (x + 1) - 2 = 0

What is the answer to 1n^2=2nlog_{10}(n) ?
The answer to 1n^2=2nlog_{10}(n) is No Solution for n\in\mathbb{R}
Solve for n: 1n^2=2nlog_{10}(n)
The solution is No Solution for n\in\mathbb{R}