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Simplifying LN(5x) + -1ln(2x + -1) = ln(4) Remove parenthesis around (5x) LN * 5x + -1ln(2x + -1) = ln(4) Reorder the terms for easier multiplication: 5LN * x + -1ln(2x + -1) = ln(4) Multiply LN * x 5xLN + -1ln(2x + -1) = ln(4) Reorder the terms: 5xLN + -1ln(-1 + 2x) = ln(4) 5xLN + (-1 * -1ln + 2x * -1ln) = ln(4) 5xLN + (1ln + -2lnx) = ln(4) Reorder the terms: 1ln + -2lnx + 5xLN = ln(4) Reorder the terms for easier multiplication: 1ln + -2lnx + 5xLN = 4ln Solving 1ln + -2lnx + 5xLN = 4ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. 1ln + -2lnx + -4ln + 5xLN = 4ln + -4ln Reorder the terms: 1ln + -4ln + -2lnx + 5xLN = 4ln + -4ln Combine like terms: 1ln + -4ln = -3ln -3ln + -2lnx + 5xLN = 4ln + -4ln Combine like terms: 4ln + -4ln = 0 -3ln + -2lnx + 5xLN = 0 Add '-5xLN' to each side of the equation. -3ln + -2lnx + 5xLN + -5xLN = 0 + -5xLN Combine like terms: 5xLN + -5xLN = 0 -3ln + -2lnx + 0 = 0 + -5xLN -3ln + -2lnx = 0 + -5xLN Remove the zero: -3ln + -2lnx = -5xLN Combine like terms: -5xLN + 5xLN = 0 -3ln + -2lnx + 5xLN = 0 The solution to this equation could not be determined.
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