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Simplifying ln(x + -3) = ln(5x) + ln(2) Reorder the terms: ln(-3 + x) = ln(5x) + ln(2) (-3 * ln + x * ln) = ln(5x) + ln(2) (-3ln + lnx) = ln(5x) + ln(2) Remove parenthesis around (5x) -3ln + lnx = ln * 5x + ln(2) Reorder the terms for easier multiplication: -3ln + lnx = 5ln * x + ln(2) Multiply ln * x -3ln + lnx = 5lnx + ln(2) Reorder the terms for easier multiplication: -3ln + lnx = 5lnx + 2ln Reorder the terms: -3ln + lnx = 2ln + 5lnx Solving -3ln + lnx = 2ln + 5lnx 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. -3ln + -2ln + lnx = 2ln + -2ln + 5lnx Combine like terms: -3ln + -2ln = -5ln -5ln + lnx = 2ln + -2ln + 5lnx Combine like terms: 2ln + -2ln = 0 -5ln + lnx = 0 + 5lnx -5ln + lnx = 5lnx Add '-5lnx' to each side of the equation. -5ln + lnx + -5lnx = 5lnx + -5lnx Combine like terms: lnx + -5lnx = -4lnx -5ln + -4lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -5ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(5 + 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 '(5 + 4x)' equal to zero and attempt to solve: Simplifying 5 + 4x = 0 Solving 5 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 0 + -5 4x = 0 + -5 Combine like terms: 0 + -5 = -5 4x = -5 Add '-4x' to each side of the equation. 4x + -4x = -5 + -4x Combine like terms: 4x + -4x = 0 0 = -5 + -4x Simplifying 0 = -5 + -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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