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Simplifying ln(x + -7) + ln(x + -3) = ln(7) Reorder the terms: ln(-7 + x) + ln(x + -3) = ln(7) (-7 * ln + x * ln) + ln(x + -3) = ln(7) (-7ln + lnx) + ln(x + -3) = ln(7) Reorder the terms: -7ln + lnx + ln(-3 + x) = ln(7) -7ln + lnx + (-3 * ln + x * ln) = ln(7) -7ln + lnx + (-3ln + lnx) = ln(7) Reorder the terms: -7ln + -3ln + lnx + lnx = ln(7) Combine like terms: -7ln + -3ln = -10ln -10ln + lnx + lnx = ln(7) Combine like terms: lnx + lnx = 2lnx -10ln + 2lnx = ln(7) Reorder the terms for easier multiplication: -10ln + 2lnx = 7ln Solving -10ln + 2lnx = 7ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7ln' to each side of the equation. -10ln + -7ln + 2lnx = 7ln + -7ln Combine like terms: -10ln + -7ln = -17ln -17ln + 2lnx = 7ln + -7ln Combine like terms: 7ln + -7ln = 0 -17ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-17 + 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 '(-17 + 2x)' equal to zero and attempt to solve: Simplifying -17 + 2x = 0 Solving -17 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + 2x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 2x = 0 + 17 2x = 0 + 17 Combine like terms: 0 + 17 = 17 2x = 17 Add '-2x' to each side of the equation. 2x + -2x = 17 + -2x Combine like terms: 2x + -2x = 0 0 = 17 + -2x Simplifying 0 = 17 + -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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