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Simplifying lnx + ln(x + -6) = ln(6x + -35) Reorder the terms: lnx + ln(-6 + x) = ln(6x + -35) lnx + (-6 * ln + x * ln) = ln(6x + -35) lnx + (-6ln + lnx) = ln(6x + -35) Reorder the terms: -6ln + lnx + lnx = ln(6x + -35) Combine like terms: lnx + lnx = 2lnx -6ln + 2lnx = ln(6x + -35) Reorder the terms: -6ln + 2lnx = ln(-35 + 6x) -6ln + 2lnx = (-35 * ln + 6x * ln) -6ln + 2lnx = (-35ln + 6lnx) Solving -6ln + 2lnx = -35ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '35ln' to each side of the equation. -6ln + 35ln + 2lnx = -35ln + 35ln + 6lnx Combine like terms: -6ln + 35ln = 29ln 29ln + 2lnx = -35ln + 35ln + 6lnx Combine like terms: -35ln + 35ln = 0 29ln + 2lnx = 0 + 6lnx 29ln + 2lnx = 6lnx Add '-6lnx' to each side of the equation. 29ln + 2lnx + -6lnx = 6lnx + -6lnx Combine like terms: 2lnx + -6lnx = -4lnx 29ln + -4lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 29ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(29 + -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 '(29 + -4x)' equal to zero and attempt to solve: Simplifying 29 + -4x = 0 Solving 29 + -4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + -4x = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -4x = 0 + -29 -4x = 0 + -29 Combine like terms: 0 + -29 = -29 -4x = -29 Add '4x' to each side of the equation. -4x + 4x = -29 + 4x Combine like terms: -4x + 4x = 0 0 = -29 + 4x Simplifying 0 = -29 + 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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