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Simplifying ln(x + -3) + ln(x + -2) = ln(12x + 24) Reorder the terms: ln(-3 + x) + ln(x + -2) = ln(12x + 24) (-3 * ln + x * ln) + ln(x + -2) = ln(12x + 24) (-3ln + lnx) + ln(x + -2) = ln(12x + 24) Reorder the terms: -3ln + lnx + ln(-2 + x) = ln(12x + 24) -3ln + lnx + (-2 * ln + x * ln) = ln(12x + 24) -3ln + lnx + (-2ln + lnx) = ln(12x + 24) Reorder the terms: -3ln + -2ln + lnx + lnx = ln(12x + 24) Combine like terms: -3ln + -2ln = -5ln -5ln + lnx + lnx = ln(12x + 24) Combine like terms: lnx + lnx = 2lnx -5ln + 2lnx = ln(12x + 24) Reorder the terms: -5ln + 2lnx = ln(24 + 12x) -5ln + 2lnx = (24 * ln + 12x * ln) -5ln + 2lnx = (24ln + 12lnx) Solving -5ln + 2lnx = 24ln + 12lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-24ln' to each side of the equation. -5ln + -24ln + 2lnx = 24ln + -24ln + 12lnx Combine like terms: -5ln + -24ln = -29ln -29ln + 2lnx = 24ln + -24ln + 12lnx Combine like terms: 24ln + -24ln = 0 -29ln + 2lnx = 0 + 12lnx -29ln + 2lnx = 12lnx Add '-12lnx' to each side of the equation. -29ln + 2lnx + -12lnx = 12lnx + -12lnx Combine like terms: 2lnx + -12lnx = -10lnx -29ln + -10lnx = 12lnx + -12lnx Combine like terms: 12lnx + -12lnx = 0 -29ln + -10lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(29 + 10x) = 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 '(29 + 10x)' equal to zero and attempt to solve: Simplifying 29 + 10x = 0 Solving 29 + 10x = 0 Move all terms containing l to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + 10x = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 10x = 0 + -29 10x = 0 + -29 Combine like terms: 0 + -29 = -29 10x = -29 Add '-10x' to each side of the equation. 10x + -10x = -29 + -10x Combine like terms: 10x + -10x = 0 0 = -29 + -10x Simplifying 0 = -29 + -10x 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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