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Simplifying ln(4x) + -1ln(24) = ln(x + -2) Remove parenthesis around (4x) ln * 4x + -1ln(24) = ln(x + -2) Reorder the terms for easier multiplication: 4ln * x + -1ln(24) = ln(x + -2) Multiply ln * x 4lnx + -1ln(24) = ln(x + -2) Reorder the terms for easier multiplication: 4lnx + -1 * 24ln = ln(x + -2) Multiply -1 * 24 4lnx + -24ln = ln(x + -2) Reorder the terms: -24ln + 4lnx = ln(x + -2) Reorder the terms: -24ln + 4lnx = ln(-2 + x) -24ln + 4lnx = (-2 * ln + x * ln) -24ln + 4lnx = (-2ln + lnx) Solving -24ln + 4lnx = -2ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2ln' to each side of the equation. -24ln + 2ln + 4lnx = -2ln + 2ln + lnx Combine like terms: -24ln + 2ln = -22ln -22ln + 4lnx = -2ln + 2ln + lnx Combine like terms: -2ln + 2ln = 0 -22ln + 4lnx = 0 + lnx -22ln + 4lnx = lnx Add '-1lnx' to each side of the equation. -22ln + 4lnx + -1lnx = lnx + -1lnx Combine like terms: 4lnx + -1lnx = 3lnx -22ln + 3lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -22ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-22 + 3x) = 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 '(-22 + 3x)' equal to zero and attempt to solve: Simplifying -22 + 3x = 0 Solving -22 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + 3x = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 3x = 0 + 22 3x = 0 + 22 Combine like terms: 0 + 22 = 22 3x = 22 Add '-3x' to each side of the equation. 3x + -3x = 22 + -3x Combine like terms: 3x + -3x = 0 0 = 22 + -3x Simplifying 0 = 22 + -3x 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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