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Simplifying ln(5x + 2) = ln(3x + 14) Reorder the terms: ln(2 + 5x) = ln(3x + 14) (2 * ln + 5x * ln) = ln(3x + 14) (2ln + 5lnx) = ln(3x + 14) Reorder the terms: 2ln + 5lnx = ln(14 + 3x) 2ln + 5lnx = (14 * ln + 3x * ln) 2ln + 5lnx = (14ln + 3lnx) Solving 2ln + 5lnx = 14ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-14ln' to each side of the equation. 2ln + -14ln + 5lnx = 14ln + -14ln + 3lnx Combine like terms: 2ln + -14ln = -12ln -12ln + 5lnx = 14ln + -14ln + 3lnx Combine like terms: 14ln + -14ln = 0 -12ln + 5lnx = 0 + 3lnx -12ln + 5lnx = 3lnx Add '-3lnx' to each side of the equation. -12ln + 5lnx + -3lnx = 3lnx + -3lnx Combine like terms: 5lnx + -3lnx = 2lnx -12ln + 2lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -12ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-6 + 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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Add '-1x' to each side of the equation. x + -1x = 6 + -1x Combine like terms: x + -1x = 0 0 = 6 + -1x Simplifying 0 = 6 + -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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