ln(2x+3)=lnx^2

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Solution for ln(2x+3)=lnx^2 equation:


Simplifying
ln(2x + 3) = lnx2

Reorder the terms:
ln(3 + 2x) = lnx2
(3 * ln + 2x * ln) = lnx2
(3ln + 2lnx) = lnx2

Solving
3ln + 2lnx = lnx2

Solving for variable 'l'.

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

Add '-1lnx2' to each side of the equation.
3ln + 2lnx + -1lnx2 = lnx2 + -1lnx2

Combine like terms: lnx2 + -1lnx2 = 0
3ln + 2lnx + -1lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(3 + 2x + -1x2) = 0

Factor a trinomial.
ln((3 + -1x)(1 + x)) = 0

Subproblem 1

Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

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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