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Simplifying ln(x + 6) + -1ln(x + -7) = ln(x) Reorder the terms: ln(6 + x) + -1ln(x + -7) = ln(x) (6 * ln + x * ln) + -1ln(x + -7) = ln(x) (6ln + lnx) + -1ln(x + -7) = ln(x) Reorder the terms: 6ln + lnx + -1ln(-7 + x) = ln(x) 6ln + lnx + (-7 * -1ln + x * -1ln) = ln(x) 6ln + lnx + (7ln + -1lnx) = ln(x) Reorder the terms: 6ln + 7ln + lnx + -1lnx = ln(x) Combine like terms: 6ln + 7ln = 13ln 13ln + lnx + -1lnx = ln(x) Combine like terms: lnx + -1lnx = 0 13ln + 0 = ln(x) 13ln = ln(x) Multiply ln * x 13ln = lnx Solving 13ln = lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx' to each side of the equation. 13ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 13ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(13 + -1x) = 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 '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Add 'x' to each side of the equation. -1x + x = -13 + x Combine like terms: -1x + x = 0 0 = -13 + x Simplifying 0 = -13 + x 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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