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Simplifying ln(x) + ln(x + -29) = ln(3) Multiply ln * x lnx + ln(x + -29) = ln(3) Reorder the terms: lnx + ln(-29 + x) = ln(3) lnx + (-29 * ln + x * ln) = ln(3) lnx + (-29ln + lnx) = ln(3) Reorder the terms: -29ln + lnx + lnx = ln(3) Combine like terms: lnx + lnx = 2lnx -29ln + 2lnx = ln(3) Reorder the terms for easier multiplication: -29ln + 2lnx = 3ln Solving -29ln + 2lnx = 3ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. -29ln + -3ln + 2lnx = 3ln + -3ln Combine like terms: -29ln + -3ln = -32ln -32ln + 2lnx = 3ln + -3ln Combine like terms: 3ln + -3ln = 0 -32ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-16 + 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 '(-16 + x)' equal to zero and attempt to solve: Simplifying -16 + x = 0 Solving -16 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 0 + 16 Combine like terms: -16 + 16 = 0 0 + x = 0 + 16 x = 0 + 16 Combine like terms: 0 + 16 = 16 x = 16 Add '-1x' to each side of the equation. x + -1x = 16 + -1x Combine like terms: x + -1x = 0 0 = 16 + -1x Simplifying 0 = 16 + -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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