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