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Simplifying ln(x + -2) + ln(x + -8) = ln * 40 Reorder the terms: ln(-2 + x) + ln(x + -8) = ln * 40 (-2 * ln + x * ln) + ln(x + -8) = ln * 40 (-2ln + lnx) + ln(x + -8) = ln * 40 Reorder the terms: -2ln + lnx + ln(-8 + x) = ln * 40 -2ln + lnx + (-8 * ln + x * ln) = ln * 40 -2ln + lnx + (-8ln + lnx) = ln * 40 Reorder the terms: -2ln + -8ln + lnx + lnx = ln * 40 Combine like terms: -2ln + -8ln = -10ln -10ln + lnx + lnx = ln * 40 Combine like terms: lnx + lnx = 2lnx -10ln + 2lnx = ln * 40 Reorder the terms for easier multiplication: -10ln + 2lnx = 40ln Solving -10ln + 2lnx = 40ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-40ln' to each side of the equation. -10ln + -40ln + 2lnx = 40ln + -40ln Combine like terms: -10ln + -40ln = -50ln -50ln + 2lnx = 40ln + -40ln Combine like terms: 40ln + -40ln = 0 -50ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-25 + x) = 0 Ignore the factor 2.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 '(-25 + x)' equal to zero and attempt to solve: Simplifying -25 + x = 0 Solving -25 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 0 + 25 Combine like terms: -25 + 25 = 0 0 + x = 0 + 25 x = 0 + 25 Combine like terms: 0 + 25 = 25 x = 25 Add '-1x' to each side of the equation. x + -1x = 25 + -1x Combine like terms: x + -1x = 0 0 = 25 + -1x Simplifying 0 = 25 + -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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