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Simplifying 3x * ln * 5 = (x + 4) * ln * 3 Reorder the terms for easier multiplication: 3 * 5x * ln = (x + 4) * ln * 3 Multiply 3 * 5 15x * ln = (x + 4) * ln * 3 Multiply x * ln 15lnx = (x + 4) * ln * 3 Reorder the terms: 15lnx = (4 + x) * ln * 3 Reorder the terms for easier multiplication: 15lnx = 3ln(4 + x) 15lnx = (4 * 3ln + x * 3ln) 15lnx = (12ln + 3lnx) Solving 15lnx = 12ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. -12ln + 15lnx = 12ln + -12ln + 3lnx Combine like terms: 12ln + -12ln = 0 -12ln + 15lnx = 0 + 3lnx -12ln + 15lnx = 3lnx Add '-3lnx' to each side of the equation. -12ln + 15lnx + -3lnx = 3lnx + -3lnx Combine like terms: 15lnx + -3lnx = 12lnx -12ln + 12lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -12ln + 12lnx = 0 Factor out the Greatest Common Factor (GCF), '12ln'. 12ln(-1 + x) = 0 Ignore the factor 12.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 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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