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Simplifying ln(3x + -4) = ln(20) + -1ln(x + -5) Reorder the terms: ln(-4 + 3x) = ln(20) + -1ln(x + -5) (-4 * ln + 3x * ln) = ln(20) + -1ln(x + -5) (-4ln + 3lnx) = ln(20) + -1ln(x + -5) Reorder the terms for easier multiplication: -4ln + 3lnx = 20ln + -1ln(x + -5) Reorder the terms: -4ln + 3lnx = 20ln + -1ln(-5 + x) -4ln + 3lnx = 20ln + (-5 * -1ln + x * -1ln) -4ln + 3lnx = 20ln + (5ln + -1lnx) Combine like terms: 20ln + 5ln = 25ln -4ln + 3lnx = 25ln + -1lnx Solving -4ln + 3lnx = 25ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-25ln' to each side of the equation. -4ln + -25ln + 3lnx = 25ln + -25ln + -1lnx Combine like terms: -4ln + -25ln = -29ln -29ln + 3lnx = 25ln + -25ln + -1lnx Combine like terms: 25ln + -25ln = 0 -29ln + 3lnx = 0 + -1lnx -29ln + 3lnx = -1lnx Add 'lnx' to each side of the equation. -29ln + 3lnx + lnx = -1lnx + lnx Combine like terms: 3lnx + lnx = 4lnx -29ln + 4lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -29ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-29 + 4x) = 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 + 4x)' equal to zero and attempt to solve: Simplifying -29 + 4x = 0 Solving -29 + 4x = 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 + 4x = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 4x = 0 + 29 4x = 0 + 29 Combine like terms: 0 + 29 = 29 4x = 29 Add '-4x' to each side of the equation. 4x + -4x = 29 + -4x Combine like terms: 4x + -4x = 0 0 = 29 + -4x Simplifying 0 = 29 + -4x 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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