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Simplifying ln(4x + 29) = ln(2x + 13) Reorder the terms: ln(29 + 4x) = ln(2x + 13) (29 * ln + 4x * ln) = ln(2x + 13) (29ln + 4lnx) = ln(2x + 13) Reorder the terms: 29ln + 4lnx = ln(13 + 2x) 29ln + 4lnx = (13 * ln + 2x * ln) 29ln + 4lnx = (13ln + 2lnx) Solving 29ln + 4lnx = 13ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-13ln' to each side of the equation. 29ln + -13ln + 4lnx = 13ln + -13ln + 2lnx Combine like terms: 29ln + -13ln = 16ln 16ln + 4lnx = 13ln + -13ln + 2lnx Combine like terms: 13ln + -13ln = 0 16ln + 4lnx = 0 + 2lnx 16ln + 4lnx = 2lnx Add '-2lnx' to each side of the equation. 16ln + 4lnx + -2lnx = 2lnx + -2lnx Combine like terms: 4lnx + -2lnx = 2lnx 16ln + 2lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 16ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(8 + x) = 0 Ignore the factor 2.Subproblem 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 '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Add '-1x' to each side of the equation. x + -1x = -8 + -1x Combine like terms: x + -1x = 0 0 = -8 + -1x Simplifying 0 = -8 + -1x 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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