What is the answer to 5x^2ln(x+1)+2ln(x+1)=0 ?

The answer to 5x^2ln(x+1)+2ln(x+1)=0 is x=0

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5x^2ln(x+1)+2ln(x+1)=0

5 x^{2} ln (x + 1) + 2 ln (x + 1) = 0

x = 0

Solution steps

5 x^{2} ln (x + 1) + 2 ln (x + 1) = 0

Factor

5 x^{2} ln (x + 1) + 2 ln (x + 1) : ln (x + 1) (5 x^{2} + 2)

ln (x + 1) (5 x^{2} + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

ln (x + 1) = 0 or 5 x^{2} + 2 = 0

Solve

ln (x + 1) = 0 : x = 0

Solve

5 x^{2} + 2 = 0 :

No Solution for

x \in R

Verify Solutions:

x = 0

True

The solution is

x = 0

x, y = p lo g_{b} (q x + r) - 8

x, lo g_{10} (x) = - 3

x, lo g_{10} (x) = - 1

9 lo g_{8} (x) = 6 + 8 lo g_{x} (8)

lo g_{10} (9 x) + lo g_{10} (x) = 4

What is the answer to 5x^2ln(x+1)+2ln(x+1)=0 ?
The answer to 5x^2ln(x+1)+2ln(x+1)=0 is x=0
Solve for x: 5x^2ln(x+1)+2ln(x+1)=0
The solution is x=0