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Simplifying ln(x) + -1ln(x + 7) = ln(4x + -28) Multiply ln * x lnx + -1ln(x + 7) = ln(4x + -28) Reorder the terms: lnx + -1ln(7 + x) = ln(4x + -28) lnx + (7 * -1ln + x * -1ln) = ln(4x + -28) lnx + (-7ln + -1lnx) = ln(4x + -28) Reorder the terms: -7ln + lnx + -1lnx = ln(4x + -28) Combine like terms: lnx + -1lnx = 0 -7ln + 0 = ln(4x + -28) -7ln = ln(4x + -28) Reorder the terms: -7ln = ln(-28 + 4x) -7ln = (-28 * ln + 4x * ln) -7ln = (-28ln + 4lnx) Solving -7ln = -28ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '28ln' to each side of the equation. -7ln + 28ln = -28ln + 28ln + 4lnx Combine like terms: -7ln + 28ln = 21ln 21ln = -28ln + 28ln + 4lnx Combine like terms: -28ln + 28ln = 0 21ln = 0 + 4lnx 21ln = 4lnx Add '-4lnx' to each side of the equation. 21ln + -4lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 21ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(21 + -4x) = 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 '(21 + -4x)' equal to zero and attempt to solve: Simplifying 21 + -4x = 0 Solving 21 + -4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -4x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -4x = 0 + -21 -4x = 0 + -21 Combine like terms: 0 + -21 = -21 -4x = -21 Add '4x' to each side of the equation. -4x + 4x = -21 + 4x Combine like terms: -4x + 4x = 0 0 = -21 + 4x Simplifying 0 = -21 + 4x 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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