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