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Simplifying ln(x + -5) = lnx + -1ln * 5 Reorder the terms: ln(-5 + x) = lnx + -1ln * 5 (-5 * ln + x * ln) = lnx + -1ln * 5 (-5ln + lnx) = lnx + -1ln * 5 Reorder the terms for easier multiplication: -5ln + lnx = lnx + -1 * 5ln Multiply -1 * 5 -5ln + lnx = lnx + -5ln Reorder the terms: -5ln + lnx = -5ln + lnx Add '5ln' to each side of the equation. -5ln + 5ln + lnx = -5ln + 5ln + lnx Combine like terms: -5ln + 5ln = 0 0 + lnx = -5ln + 5ln + lnx lnx = -5ln + 5ln + lnx Combine like terms: -5ln + 5ln = 0 lnx = 0 + lnx lnx = lnx Add '-1lnx' to each side of the equation. lnx + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 0 = lnx + -1lnx Combine like terms: lnx + -1lnx = 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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