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Simplifying ln(x + -2) + -1ln(x + 3) = ln(x + 1) + -1ln(x + 6) Reorder the terms: ln(-2 + x) + -1ln(x + 3) = ln(x + 1) + -1ln(x + 6) (-2 * ln + x * ln) + -1ln(x + 3) = ln(x + 1) + -1ln(x + 6) (-2ln + lnx) + -1ln(x + 3) = ln(x + 1) + -1ln(x + 6) Reorder the terms: -2ln + lnx + -1ln(3 + x) = ln(x + 1) + -1ln(x + 6) -2ln + lnx + (3 * -1ln + x * -1ln) = ln(x + 1) + -1ln(x + 6) -2ln + lnx + (-3ln + -1lnx) = ln(x + 1) + -1ln(x + 6) Reorder the terms: -2ln + -3ln + lnx + -1lnx = ln(x + 1) + -1ln(x + 6) Combine like terms: -2ln + -3ln = -5ln -5ln + lnx + -1lnx = ln(x + 1) + -1ln(x + 6) Combine like terms: lnx + -1lnx = 0 -5ln + 0 = ln(x + 1) + -1ln(x + 6) -5ln = ln(x + 1) + -1ln(x + 6) Reorder the terms: -5ln = ln(1 + x) + -1ln(x + 6) -5ln = (1 * ln + x * ln) + -1ln(x + 6) -5ln = (1ln + lnx) + -1ln(x + 6) Reorder the terms: -5ln = 1ln + lnx + -1ln(6 + x) -5ln = 1ln + lnx + (6 * -1ln + x * -1ln) -5ln = 1ln + lnx + (-6ln + -1lnx) Reorder the terms: -5ln = 1ln + -6ln + lnx + -1lnx Combine like terms: 1ln + -6ln = -5ln -5ln = -5ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -5ln = -5ln + 0 -5ln = -5ln Add '5ln' to each side of the equation. -5ln + 5ln = -5ln + 5ln Combine like terms: -5ln + 5ln = 0 0 = -5ln + 5ln Combine like terms: -5ln + 5ln = 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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