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Simplifying ln(5x + -3) + ln(2) = ln(24 + -2x) Reorder the terms: ln(-3 + 5x) + ln(2) = ln(24 + -2x) (-3 * ln + 5x * ln) + ln(2) = ln(24 + -2x) (-3ln + 5lnx) + ln(2) = ln(24 + -2x) Reorder the terms for easier multiplication: -3ln + 5lnx + 2ln = ln(24 + -2x) Reorder the terms: -3ln + 2ln + 5lnx = ln(24 + -2x) Combine like terms: -3ln + 2ln = -1ln -1ln + 5lnx = ln(24 + -2x) -1ln + 5lnx = (24 * ln + -2x * ln) -1ln + 5lnx = (24ln + -2lnx) Solving -1ln + 5lnx = 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 + 5lnx = 24ln + -24ln + -2lnx Combine like terms: -1ln + -24ln = -25ln -25ln + 5lnx = 24ln + -24ln + -2lnx Combine like terms: 24ln + -24ln = 0 -25ln + 5lnx = 0 + -2lnx -25ln + 5lnx = -2lnx Add '2lnx' to each side of the equation. -25ln + 5lnx + 2lnx = -2lnx + 2lnx Combine like terms: 5lnx + 2lnx = 7lnx -25ln + 7lnx = -2lnx + 2lnx Combine like terms: -2lnx + 2lnx = 0 -25ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-25 + 7x) = 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 + 7x)' equal to zero and attempt to solve: Simplifying -25 + 7x = 0 Solving -25 + 7x = 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 + 7x = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 7x = 0 + 25 7x = 0 + 25 Combine like terms: 0 + 25 = 25 7x = 25 Add '-7x' to each side of the equation. 7x + -7x = 25 + -7x Combine like terms: 7x + -7x = 0 0 = 25 + -7x Simplifying 0 = 25 + -7x 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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