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Simplifying ln(3x + -5) + -1ln(4x) = 1 Reorder the terms: ln(-5 + 3x) + -1ln(4x) = 1 (-5 * ln + 3x * ln) + -1ln(4x) = 1 (-5ln + 3lnx) + -1ln(4x) = 1 Remove parenthesis around (4x) -5ln + 3lnx + -1ln * 4x = 1 Reorder the terms for easier multiplication: -5ln + 3lnx + -1 * 4ln * x = 1 Multiply -1 * 4 -5ln + 3lnx + -4ln * x = 1 Multiply ln * x -5ln + 3lnx + -4lnx = 1 Combine like terms: 3lnx + -4lnx = -1lnx -5ln + -1lnx = 1 Solving -5ln + -1lnx = 1 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Reorder the terms: -1 + -5ln + -1lnx = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -5ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 5ln + lnx) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 5ln + lnx)' equal to zero and attempt to solve: Simplifying 1 + 5ln + lnx = 0 Solving 1 + 5ln + lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 5ln + -1 + lnx = 0 + -1 Reorder the terms: 1 + -1 + 5ln + lnx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5ln + lnx = 0 + -1 5ln + lnx = 0 + -1 Combine like terms: 0 + -1 = -1 5ln + lnx = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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