ln(x^2+2x)=lnx

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Solution for ln(x^2+2x)=lnx equation:


Simplifying
ln(x2 + 2x) = lnx

Reorder the terms:
ln(2x + x2) = lnx
(2x * ln + x2 * ln) = lnx
(2lnx + lnx2) = lnx

Solving
2lnx + lnx2 = lnx

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-1lnx' to each side of the equation.
2lnx + -1lnx + lnx2 = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
1lnx + lnx2 = lnx + -1lnx

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

Factor out the Greatest Common Factor (GCF), 'lnx'.
lnx(1 + x) = 0

Subproblem 1

Set the factor 'lnx' equal to zero and attempt to solve: Simplifying lnx = 0 Solving lnx = 0 Move all terms containing l to the left, all other terms to the right. Simplifying lnx = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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