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Simplifying ln(x + 3) = ln2(x + -2) + -1ln(x + -4) Reorder the terms: ln(3 + x) = ln2(x + -2) + -1ln(x + -4) (3 * ln + x * ln) = ln2(x + -2) + -1ln(x + -4) (3ln + lnx) = ln2(x + -2) + -1ln(x + -4) Reorder the terms: 3ln + lnx = ln2(-2 + x) + -1ln(x + -4) 3ln + lnx = (-2 * ln2 + x * ln2) + -1ln(x + -4) 3ln + lnx = (-2ln2 + ln2x) + -1ln(x + -4) Reorder the terms: 3ln + lnx = -2ln2 + ln2x + -1ln(-4 + x) 3ln + lnx = -2ln2 + ln2x + (-4 * -1ln + x * -1ln) 3ln + lnx = -2ln2 + ln2x + (4ln + -1lnx) Reorder the terms: 3ln + lnx = 4ln + -1lnx + -2ln2 + ln2x Solving 3ln + lnx = 4ln + -1lnx + -2ln2 + ln2x Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. 3ln + -4ln + lnx = 4ln + -1lnx + -2ln2 + -4ln + ln2x Combine like terms: 3ln + -4ln = -1ln -1ln + lnx = 4ln + -1lnx + -2ln2 + -4ln + ln2x Reorder the terms: -1ln + lnx = 4ln + -4ln + -1lnx + -2ln2 + ln2x Combine like terms: 4ln + -4ln = 0 -1ln + lnx = 0 + -1lnx + -2ln2 + ln2x -1ln + lnx = -1lnx + -2ln2 + ln2x Add 'lnx' to each side of the equation. -1ln + lnx + lnx = -1lnx + -2ln2 + lnx + ln2x Combine like terms: lnx + lnx = 2lnx -1ln + 2lnx = -1lnx + -2ln2 + lnx + ln2x Reorder the terms: -1ln + 2lnx = -1lnx + lnx + -2ln2 + ln2x Combine like terms: -1lnx + lnx = 0 -1ln + 2lnx = 0 + -2ln2 + ln2x -1ln + 2lnx = -2ln2 + ln2x Add '2ln2' to each side of the equation. -1ln + 2lnx + 2ln2 = -2ln2 + 2ln2 + ln2x Combine like terms: -2ln2 + 2ln2 = 0 -1ln + 2lnx + 2ln2 = 0 + ln2x -1ln + 2lnx + 2ln2 = ln2x Add '-1ln2x' to each side of the equation. -1ln + 2lnx + 2ln2 + -1ln2x = ln2x + -1ln2x Combine like terms: ln2x + -1ln2x = 0 -1ln + 2lnx + 2ln2 + -1ln2x = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-1 + 2x + 2n + -1nx) = 0Subproblem 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 '(-1 + 2x + 2n + -1nx)' equal to zero and attempt to solve: Simplifying -1 + 2x + 2n + -1nx = 0 Reorder the terms: -1 + 2n + -1nx + 2x = 0 Solving -1 + 2n + -1nx + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 2n + -1nx + 1 + 2x = 0 + 1 Reorder the terms: -1 + 1 + 2n + -1nx + 2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2n + -1nx + 2x = 0 + 1 2n + -1nx + 2x = 0 + 1 Combine like terms: 0 + 1 = 1 2n + -1nx + 2x = 1 Add '-2n' to each side of the equation. 2n + -1nx + -2n + 2x = 1 + -2n Reorder the terms: 2n + -2n + -1nx + 2x = 1 + -2n Combine like terms: 2n + -2n = 0 0 + -1nx + 2x = 1 + -2n -1nx + 2x = 1 + -2n Add 'nx' to each side of the equation. -1nx + nx + 2x = 1 + -2n + nx Combine like terms: -1nx + nx = 0 0 + 2x = 1 + -2n + nx 2x = 1 + -2n + nx Add '-2x' to each side of the equation. 2x + -2x = 1 + -2n + nx + -2x Combine like terms: 2x + -2x = 0 0 = 1 + -2n + nx + -2x Simplifying 0 = 1 + -2n + nx + -2x 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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