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Simplifying ln(4x + 1) = ln(2x + 5) Reorder the terms: ln(1 + 4x) = ln(2x + 5) (1 * ln + 4x * ln) = ln(2x + 5) (1ln + 4lnx) = ln(2x + 5) Reorder the terms: 1ln + 4lnx = ln(5 + 2x) 1ln + 4lnx = (5 * ln + 2x * ln) 1ln + 4lnx = (5ln + 2lnx) Solving 1ln + 4lnx = 5ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. 1ln + -5ln + 4lnx = 5ln + -5ln + 2lnx Combine like terms: 1ln + -5ln = -4ln -4ln + 4lnx = 5ln + -5ln + 2lnx Combine like terms: 5ln + -5ln = 0 -4ln + 4lnx = 0 + 2lnx -4ln + 4lnx = 2lnx Add '-2lnx' to each side of the equation. -4ln + 4lnx + -2lnx = 2lnx + -2lnx Combine like terms: 4lnx + -2lnx = 2lnx -4ln + 2lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -4ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-2 + 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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -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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