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