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Simplifying lnx + ln(x + -6) = ln(7x + -40) Reorder the terms: lnx + ln(-6 + x) = ln(7x + -40) lnx + (-6 * ln + x * ln) = ln(7x + -40) lnx + (-6ln + lnx) = ln(7x + -40) Reorder the terms: -6ln + lnx + lnx = ln(7x + -40) Combine like terms: lnx + lnx = 2lnx -6ln + 2lnx = ln(7x + -40) Reorder the terms: -6ln + 2lnx = ln(-40 + 7x) -6ln + 2lnx = (-40 * ln + 7x * ln) -6ln + 2lnx = (-40ln + 7lnx) Solving -6ln + 2lnx = -40ln + 7lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '40ln' to each side of the equation. -6ln + 40ln + 2lnx = -40ln + 40ln + 7lnx Combine like terms: -6ln + 40ln = 34ln 34ln + 2lnx = -40ln + 40ln + 7lnx Combine like terms: -40ln + 40ln = 0 34ln + 2lnx = 0 + 7lnx 34ln + 2lnx = 7lnx Add '-7lnx' to each side of the equation. 34ln + 2lnx + -7lnx = 7lnx + -7lnx Combine like terms: 2lnx + -7lnx = -5lnx 34ln + -5lnx = 7lnx + -7lnx Combine like terms: 7lnx + -7lnx = 0 34ln + -5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(34 + -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 '(34 + -5x)' equal to zero and attempt to solve: Simplifying 34 + -5x = 0 Solving 34 + -5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-34' to each side of the equation. 34 + -34 + -5x = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -5x = 0 + -34 -5x = 0 + -34 Combine like terms: 0 + -34 = -34 -5x = -34 Add '5x' to each side of the equation. -5x + 5x = -34 + 5x Combine like terms: -5x + 5x = 0 0 = -34 + 5x Simplifying 0 = -34 + 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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