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Simplifying ln(12) + ln(x) = ln(12 + x) Reorder the terms for easier multiplication: 12ln + ln(x) = ln(12 + x) Multiply ln * x 12ln + lnx = ln(12 + x) 12ln + lnx = (12 * ln + x * ln) 12ln + lnx = (12ln + lnx) Add '-12ln' to each side of the equation. 12ln + -12ln + lnx = 12ln + -12ln + lnx Combine like terms: 12ln + -12ln = 0 0 + lnx = 12ln + -12ln + lnx lnx = 12ln + -12ln + lnx Combine like terms: 12ln + -12ln = 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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