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Simplifying ln(x + 2) + ln(x + -1) = ln(10) Reorder the terms: ln(2 + x) + ln(x + -1) = ln(10) (2 * ln + x * ln) + ln(x + -1) = ln(10) (2ln + lnx) + ln(x + -1) = ln(10) Reorder the terms: 2ln + lnx + ln(-1 + x) = ln(10) 2ln + lnx + (-1 * ln + x * ln) = ln(10) 2ln + lnx + (-1ln + lnx) = ln(10) Reorder the terms: 2ln + -1ln + lnx + lnx = ln(10) Combine like terms: 2ln + -1ln = 1ln 1ln + lnx + lnx = ln(10) Combine like terms: lnx + lnx = 2lnx 1ln + 2lnx = ln(10) Reorder the terms for easier multiplication: 1ln + 2lnx = 10ln Solving 1ln + 2lnx = 10ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. 1ln + -10ln + 2lnx = 10ln + -10ln Combine like terms: 1ln + -10ln = -9ln -9ln + 2lnx = 10ln + -10ln Combine like terms: 10ln + -10ln = 0 -9ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-9 + 2x) = 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 '(-9 + 2x)' equal to zero and attempt to solve: Simplifying -9 + 2x = 0 Solving -9 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2x = 0 + 9 2x = 0 + 9 Combine like terms: 0 + 9 = 9 2x = 9 Add '-2x' to each side of the equation. 2x + -2x = 9 + -2x Combine like terms: 2x + -2x = 0 0 = 9 + -2x Simplifying 0 = 9 + -2x 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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