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Simplifying ln(4) + ln = ln(5) + ln(4x + -4) Reorder the terms for easier multiplication: 4ln + ln = ln(5) + ln(4x + -4) Combine like terms: 4ln + ln = 5ln 5ln = ln(5) + ln(4x + -4) Reorder the terms for easier multiplication: 5ln = 5ln + ln(4x + -4) Reorder the terms: 5ln = 5ln + ln(-4 + 4x) 5ln = 5ln + (-4 * ln + 4x * ln) 5ln = 5ln + (-4ln + 4lnx) Combine like terms: 5ln + -4ln = 1ln 5ln = 1ln + 4lnx Solving 5ln = 1ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. 5ln + -1ln = 1ln + -1ln + 4lnx Combine like terms: 5ln + -1ln = 4ln 4ln = 1ln + -1ln + 4lnx Combine like terms: 1ln + -1ln = 0 4ln = 0 + 4lnx 4ln = 4lnx Add '-4lnx' to each side of the equation. 4ln + -4lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 4ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '4ln'. 4ln(1 + -1x) = 0 Ignore the factor 4.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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x 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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