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Simplifying 2ln(x) + -1ln(x + 5) = ln(x) + -1ln(3) Multiply ln * x 2lnx + -1ln(x + 5) = ln(x) + -1ln(3) Reorder the terms: 2lnx + -1ln(5 + x) = ln(x) + -1ln(3) 2lnx + (5 * -1ln + x * -1ln) = ln(x) + -1ln(3) 2lnx + (-5ln + -1lnx) = ln(x) + -1ln(3) Reorder the terms: -5ln + 2lnx + -1lnx = ln(x) + -1ln(3) Combine like terms: 2lnx + -1lnx = 1lnx -5ln + 1lnx = ln(x) + -1ln(3) Multiply ln * x -5ln + 1lnx = lnx + -1ln(3) Reorder the terms for easier multiplication: -5ln + 1lnx = lnx + -1 * 3ln Multiply -1 * 3 -5ln + 1lnx = lnx + -3ln Reorder the terms: -5ln + 1lnx = -3ln + lnx Solving -5ln + 1lnx = -3ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '3ln' to each side of the equation. -5ln + 3ln + 1lnx = -3ln + 3ln + lnx Combine like terms: -5ln + 3ln = -2ln -2ln + 1lnx = -3ln + 3ln + lnx Combine like terms: -3ln + 3ln = 0 -2ln + 1lnx = 0 + lnx -2ln + 1lnx = lnx Add '-1lnx' to each side of the equation. -2ln + 1lnx + -1lnx = lnx + -1lnx Combine like terms: 1lnx + -1lnx = 0 -2ln + 0 = lnx + -1lnx -2ln = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -2ln = 0 Divide each side by '-2'. ln = 0 Simplifying ln = 0 The solution to this equation could not be determined.
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