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Simplifying ln(x) + ln(x + -5) = ln(24) Multiply ln * x lnx + ln(x + -5) = ln(24) Reorder the terms: lnx + ln(-5 + x) = ln(24) lnx + (-5 * ln + x * ln) = ln(24) lnx + (-5ln + lnx) = ln(24) Reorder the terms: -5ln + lnx + lnx = ln(24) Combine like terms: lnx + lnx = 2lnx -5ln + 2lnx = ln(24) Reorder the terms for easier multiplication: -5ln + 2lnx = 24ln Solving -5ln + 2lnx = 24ln 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 Combine like terms: -5ln + -24ln = -29ln -29ln + 2lnx = 24ln + -24ln Combine like terms: 24ln + -24ln = 0 -29ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-29 + 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 '(-29 + 2x)' equal to zero and attempt to solve: Simplifying -29 + 2x = 0 Solving -29 + 2x = 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 + 2x = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 2x = 0 + 29 2x = 0 + 29 Combine like terms: 0 + 29 = 29 2x = 29 Add '-2x' to each side of the equation. 2x + -2x = 29 + -2x Combine like terms: 2x + -2x = 0 0 = 29 + -2x Simplifying 0 = 29 + -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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