(x+1)*ln(x)-x*ln(x+1)=0

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Solution for (x+1)*ln(x)-x*ln(x+1)=0 equation:


Simplifying
(x + 1) * ln(x) + -1x * ln(x + 1) = 0

Reorder the terms:
(1 + x) * ln(x) + -1x * ln(x + 1) = 0

Reorder the terms for easier multiplication:
ln * x(1 + x) + -1x * ln(x + 1) = 0

Multiply ln * x
lnx(1 + x) + -1x * ln(x + 1) = 0
(1 * lnx + x * lnx) + -1x * ln(x + 1) = 0
(1lnx + lnx2) + -1x * ln(x + 1) = 0

Reorder the terms:
1lnx + lnx2 + -1x * ln(1 + x) = 0

Multiply x * ln
1lnx + lnx2 + -1lnx(1 + x) = 0
1lnx + lnx2 + (1 * -1lnx + x * -1lnx) = 0
1lnx + lnx2 + (-1lnx + -1lnx2) = 0

Reorder the terms:
1lnx + -1lnx + lnx2 + -1lnx2 = 0

Combine like terms: 1lnx + -1lnx = 0
0 + lnx2 + -1lnx2 = 0
lnx2 + -1lnx2 = 0

Combine like terms: lnx2 + -1lnx2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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