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