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

The answer to 2(x+1)ln(x+1)+(x+1)=0 is x= 1/(sqrt(e))-1

Solve for x: 2(x+1)ln(x+1)+(x+1)=0

The solution is x= 1/(sqrt(e))-1

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

x = \frac{1}{e} - 1

Solution steps

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

Move

x

to the right side

2 (x + 1) ln (x + 1) + 1 = - x

Move

1

to the right side

2 (x + 1) ln (x + 1) = - x - 1

Subtract

- x - 1

from both sides

2 (x + 1) ln (x + 1) - (- x - 1) = - x - 1 - (- x - 1)

Simplify

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

Factor

2 x ln (x + 1) + 2 ln (x + 1) + x + 1 : (1 + x) (2 ln (x + 1) + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

1 + x = 0 or 2 ln (x + 1) + 1 = 0

Solve

1 + x = 0 : x = - 1

Solve

2 ln (x + 1) + 1 = 0 : x = \frac{1}{e} - 1

Verify Solutions:

x = - 1

False

, x = \frac{1}{e} - 1

True

The solution is

x = \frac{1}{e} - 1

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

lo g_{4} (x + 3) = lo g_{4} (3 x - 7)

1 0^{7 l o g_{10} (x)} = 7 x

35000 = 95858 ln (x) - 991636

lo g_{4} (2 - x) = lo g_{16} (25)

What is the answer to 2(x+1)ln(x+1)+(x+1)=0 ?
The answer to 2(x+1)ln(x+1)+(x+1)=0 is x= 1/(sqrt(e))-1
Solve for x: 2(x+1)ln(x+1)+(x+1)=0
The solution is x= 1/(sqrt(e))-1