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Simplifying ln(1 + -1x) + ln(7 + -6) = ln(16) (1 * ln + -1x * ln) + ln(7 + -6) = ln(16) (1ln + -1lnx) + ln(7 + -6) = ln(16) Combine like terms: 7 + -6 = 1 1ln + -1lnx + ln(1) = ln(16) Reorder the terms for easier multiplication: 1ln + -1lnx + 1ln = ln(16) Reorder the terms: 1ln + 1ln + -1lnx = ln(16) Combine like terms: 1ln + 1ln = 2ln 2ln + -1lnx = ln(16) Reorder the terms for easier multiplication: 2ln + -1lnx = 16ln Solving 2ln + -1lnx = 16ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-16ln' to each side of the equation. 2ln + -16ln + -1lnx = 16ln + -16ln Combine like terms: 2ln + -16ln = -14ln -14ln + -1lnx = 16ln + -16ln Combine like terms: 16ln + -16ln = 0 -14ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(14 + 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 '(14 + x)' equal to zero and attempt to solve: Simplifying 14 + x = 0 Solving 14 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + x = 0 + -14 x = 0 + -14 Combine like terms: 0 + -14 = -14 x = -14 Add '-1x' to each side of the equation. x + -1x = -14 + -1x Combine like terms: x + -1x = 0 0 = -14 + -1x Simplifying 0 = -14 + -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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