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Simplifying ln(x + -2) + ln(3) = ln(5x + -7) Reorder the terms: ln(-2 + x) + ln(3) = ln(5x + -7) (-2 * ln + x * ln) + ln(3) = ln(5x + -7) (-2ln + lnx) + ln(3) = ln(5x + -7) Reorder the terms for easier multiplication: -2ln + lnx + 3ln = ln(5x + -7) Reorder the terms: -2ln + 3ln + lnx = ln(5x + -7) Combine like terms: -2ln + 3ln = 1ln 1ln + lnx = ln(5x + -7) Reorder the terms: 1ln + lnx = ln(-7 + 5x) 1ln + lnx = (-7 * ln + 5x * ln) 1ln + lnx = (-7ln + 5lnx) Solving 1ln + lnx = -7ln + 5lnx 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. 1ln + 7ln + lnx = -7ln + 7ln + 5lnx Combine like terms: 1ln + 7ln = 8ln 8ln + lnx = -7ln + 7ln + 5lnx Combine like terms: -7ln + 7ln = 0 8ln + lnx = 0 + 5lnx 8ln + lnx = 5lnx Add '-5lnx' to each side of the equation. 8ln + lnx + -5lnx = 5lnx + -5lnx Combine like terms: lnx + -5lnx = -4lnx 8ln + -4lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 8ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '4ln'. 4ln(2 + -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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + 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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