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Simplifying ln(2) + ln(x + 1) = ln(4x + -7) Reorder the terms for easier multiplication: 2ln + ln(x + 1) = ln(4x + -7) Reorder the terms: 2ln + ln(1 + x) = ln(4x + -7) 2ln + (1 * ln + x * ln) = ln(4x + -7) 2ln + (1ln + lnx) = ln(4x + -7) Combine like terms: 2ln + 1ln = 3ln 3ln + lnx = ln(4x + -7) Reorder the terms: 3ln + lnx = ln(-7 + 4x) 3ln + lnx = (-7 * ln + 4x * ln) 3ln + lnx = (-7ln + 4lnx) Solving 3ln + lnx = -7ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '7ln' to each side of the equation. 3ln + 7ln + lnx = -7ln + 7ln + 4lnx Combine like terms: 3ln + 7ln = 10ln 10ln + lnx = -7ln + 7ln + 4lnx Combine like terms: -7ln + 7ln = 0 10ln + lnx = 0 + 4lnx 10ln + lnx = 4lnx Add '-4lnx' to each side of the equation. 10ln + lnx + -4lnx = 4lnx + -4lnx Combine like terms: lnx + -4lnx = -3lnx 10ln + -3lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 10ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(10 + -3x) = 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 '(10 + -3x)' equal to zero and attempt to solve: Simplifying 10 + -3x = 0 Solving 10 + -3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3x = 0 + -10 -3x = 0 + -10 Combine like terms: 0 + -10 = -10 -3x = -10 Add '3x' to each side of the equation. -3x + 3x = -10 + 3x Combine like terms: -3x + 3x = 0 0 = -10 + 3x Simplifying 0 = -10 + 3x 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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