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Simplifying ln(2x + 5) + 3lnx + -1lnx = ln(6x + 15) Reorder the terms: ln(5 + 2x) + 3lnx + -1lnx = ln(6x + 15) (5 * ln + 2x * ln) + 3lnx + -1lnx = ln(6x + 15) (5ln + 2lnx) + 3lnx + -1lnx = ln(6x + 15) Combine like terms: 2lnx + 3lnx = 5lnx 5ln + 5lnx + -1lnx = ln(6x + 15) Combine like terms: 5lnx + -1lnx = 4lnx 5ln + 4lnx = ln(6x + 15) Reorder the terms: 5ln + 4lnx = ln(15 + 6x) 5ln + 4lnx = (15 * ln + 6x * ln) 5ln + 4lnx = (15ln + 6lnx) Solving 5ln + 4lnx = 15ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-15ln' to each side of the equation. 5ln + -15ln + 4lnx = 15ln + -15ln + 6lnx Combine like terms: 5ln + -15ln = -10ln -10ln + 4lnx = 15ln + -15ln + 6lnx Combine like terms: 15ln + -15ln = 0 -10ln + 4lnx = 0 + 6lnx -10ln + 4lnx = 6lnx Add '-6lnx' to each side of the equation. -10ln + 4lnx + -6lnx = 6lnx + -6lnx Combine like terms: 4lnx + -6lnx = -2lnx -10ln + -2lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -10ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(5 + 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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -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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