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Simplifying ln(3 + -3) + ln(3 + -2) = ln(2x + -24) Combine like terms: 3 + -3 = 0 ln(0) + ln(3 + -2) = ln(2x + -24) Reorder the terms for easier multiplication: 0ln + ln(3 + -2) = ln(2x + -24) Anything times zero is zero. 0ln + ln(3 + -2) = ln(2x + -24) Combine like terms: 3 + -2 = 1 0 + ln(1) = ln(2x + -24) Reorder the terms for easier multiplication: 0 + 1ln = ln(2x + -24) Remove the zero: 1ln = ln(2x + -24) Reorder the terms: 1ln = ln(-24 + 2x) 1ln = (-24 * ln + 2x * ln) 1ln = (-24ln + 2lnx) Solving 1ln = -24ln + 2lnx 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. 1ln + 24ln = -24ln + 24ln + 2lnx Combine like terms: 1ln + 24ln = 25ln 25ln = -24ln + 24ln + 2lnx Combine like terms: -24ln + 24ln = 0 25ln = 0 + 2lnx 25ln = 2lnx Add '-2lnx' to each side of the equation. 25ln + -2lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 25ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(25 + -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 '(25 + -2x)' equal to zero and attempt to solve: Simplifying 25 + -2x = 0 Solving 25 + -2x = 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 + -2x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -2x = 0 + -25 -2x = 0 + -25 Combine like terms: 0 + -25 = -25 -2x = -25 Add '2x' to each side of the equation. -2x + 2x = -25 + 2x Combine like terms: -2x + 2x = 0 0 = -25 + 2x Simplifying 0 = -25 + 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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