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Simplifying ln(4x + -3) + -1ln * 2 = ln(24 + -3x) Reorder the terms: ln(-3 + 4x) + -1ln * 2 = ln(24 + -3x) (-3 * ln + 4x * ln) + -1ln * 2 = ln(24 + -3x) (-3ln + 4lnx) + -1ln * 2 = ln(24 + -3x) Reorder the terms for easier multiplication: -3ln + 4lnx + -1 * 2ln = ln(24 + -3x) Multiply -1 * 2 -3ln + 4lnx + -2ln = ln(24 + -3x) Reorder the terms: -3ln + -2ln + 4lnx = ln(24 + -3x) Combine like terms: -3ln + -2ln = -5ln -5ln + 4lnx = ln(24 + -3x) -5ln + 4lnx = (24 * ln + -3x * ln) -5ln + 4lnx = (24ln + -3lnx) Solving -5ln + 4lnx = 24ln + -3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-24ln' to each side of the equation. -5ln + -24ln + 4lnx = 24ln + -24ln + -3lnx Combine like terms: -5ln + -24ln = -29ln -29ln + 4lnx = 24ln + -24ln + -3lnx Combine like terms: 24ln + -24ln = 0 -29ln + 4lnx = 0 + -3lnx -29ln + 4lnx = -3lnx Add '3lnx' to each side of the equation. -29ln + 4lnx + 3lnx = -3lnx + 3lnx Combine like terms: 4lnx + 3lnx = 7lnx -29ln + 7lnx = -3lnx + 3lnx Combine like terms: -3lnx + 3lnx = 0 -29ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-29 + 7x) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-29 + 7x)' equal to zero and attempt to solve: Simplifying -29 + 7x = 0 Solving -29 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '29' to each side of the equation. -29 + 29 + 7x = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 7x = 0 + 29 7x = 0 + 29 Combine like terms: 0 + 29 = 29 7x = 29 Add '-7x' to each side of the equation. 7x + -7x = 29 + -7x Combine like terms: 7x + -7x = 0 0 = 29 + -7x Simplifying 0 = 29 + -7x 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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