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Simplifying ln(x + -7) = ln(2x + 5) Reorder the terms: ln(-7 + x) = ln(2x + 5) (-7 * ln + x * ln) = ln(2x + 5) (-7ln + lnx) = ln(2x + 5) Reorder the terms: -7ln + lnx = ln(5 + 2x) -7ln + lnx = (5 * ln + 2x * ln) -7ln + lnx = (5ln + 2lnx) Solving -7ln + lnx = 5ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. -7ln + -5ln + lnx = 5ln + -5ln + 2lnx Combine like terms: -7ln + -5ln = -12ln -12ln + lnx = 5ln + -5ln + 2lnx Combine like terms: 5ln + -5ln = 0 -12ln + lnx = 0 + 2lnx -12ln + lnx = 2lnx Add '-2lnx' to each side of the equation. -12ln + lnx + -2lnx = 2lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx -12ln + -1lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -12ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(12 + x) = 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 '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Add '-1x' to each side of the equation. x + -1x = -12 + -1x Combine like terms: x + -1x = 0 0 = -12 + -1x Simplifying 0 = -12 + -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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