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Simplifying ln(x + -3) + ln(x) = ln(24 + -1x) Reorder the terms: ln(-3 + x) + ln(x) = ln(24 + -1x) (-3 * ln + x * ln) + ln(x) = ln(24 + -1x) (-3ln + lnx) + ln(x) = ln(24 + -1x) Multiply ln * x -3ln + lnx + lnx = ln(24 + -1x) Combine like terms: lnx + lnx = 2lnx -3ln + 2lnx = ln(24 + -1x) -3ln + 2lnx = (24 * ln + -1x * ln) -3ln + 2lnx = (24ln + -1lnx) Solving -3ln + 2lnx = 24ln + -1lnx 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. -3ln + -24ln + 2lnx = 24ln + -24ln + -1lnx Combine like terms: -3ln + -24ln = -27ln -27ln + 2lnx = 24ln + -24ln + -1lnx Combine like terms: 24ln + -24ln = 0 -27ln + 2lnx = 0 + -1lnx -27ln + 2lnx = -1lnx Add 'lnx' to each side of the equation. -27ln + 2lnx + lnx = -1lnx + lnx Combine like terms: 2lnx + lnx = 3lnx -27ln + 3lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -27ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-9 + x) = 0 Ignore the factor 3.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 '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 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 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Add '-1x' to each side of the equation. x + -1x = 9 + -1x Combine like terms: x + -1x = 0 0 = 9 + -1x Simplifying 0 = 9 + -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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