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Simplifying ln(7x + -4) = ln(2x + -11) Reorder the terms: ln(-4 + 7x) = ln(2x + -11) (-4 * ln + 7x * ln) = ln(2x + -11) (-4ln + 7lnx) = ln(2x + -11) Reorder the terms: -4ln + 7lnx = ln(-11 + 2x) -4ln + 7lnx = (-11 * ln + 2x * ln) -4ln + 7lnx = (-11ln + 2lnx) Solving -4ln + 7lnx = -11ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '11ln' to each side of the equation. -4ln + 11ln + 7lnx = -11ln + 11ln + 2lnx Combine like terms: -4ln + 11ln = 7ln 7ln + 7lnx = -11ln + 11ln + 2lnx Combine like terms: -11ln + 11ln = 0 7ln + 7lnx = 0 + 2lnx 7ln + 7lnx = 2lnx Add '-2lnx' to each side of the equation. 7ln + 7lnx + -2lnx = 2lnx + -2lnx Combine like terms: 7lnx + -2lnx = 5lnx 7ln + 5lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 7ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(7 + 5x) = 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 '(7 + 5x)' equal to zero and attempt to solve: Simplifying 7 + 5x = 0 Solving 7 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5x = 0 + -7 5x = 0 + -7 Combine like terms: 0 + -7 = -7 5x = -7 Add '-5x' to each side of the equation. 5x + -5x = -7 + -5x Combine like terms: 5x + -5x = 0 0 = -7 + -5x Simplifying 0 = -7 + -5x 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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