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

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

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

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

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

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

Decimal Notation

x = - 0.39346 \dots

Solution steps

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

Switch sides

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

lo g_{4} (x) = 8

lo g_{3} (y) = 3

lo g_{10} (x) - lo g_{10} (x + 2) = - 2

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

a, lo g_{a + 2 b} (3) = 2

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