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Simplifying ln(6x + -5) = ln * 30 + -1ln(x + -6) Reorder the terms: ln(-5 + 6x) = ln * 30 + -1ln(x + -6) (-5 * ln + 6x * ln) = ln * 30 + -1ln(x + -6) (-5ln + 6lnx) = ln * 30 + -1ln(x + -6) Reorder the terms for easier multiplication: -5ln + 6lnx = 30ln + -1ln(x + -6) Reorder the terms: -5ln + 6lnx = 30ln + -1ln(-6 + x) -5ln + 6lnx = 30ln + (-6 * -1ln + x * -1ln) -5ln + 6lnx = 30ln + (6ln + -1lnx) Combine like terms: 30ln + 6ln = 36ln -5ln + 6lnx = 36ln + -1lnx Solving -5ln + 6lnx = 36ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-36ln' to each side of the equation. -5ln + -36ln + 6lnx = 36ln + -36ln + -1lnx Combine like terms: -5ln + -36ln = -41ln -41ln + 6lnx = 36ln + -36ln + -1lnx Combine like terms: 36ln + -36ln = 0 -41ln + 6lnx = 0 + -1lnx -41ln + 6lnx = -1lnx Add 'lnx' to each side of the equation. -41ln + 6lnx + lnx = -1lnx + lnx Combine like terms: 6lnx + lnx = 7lnx -41ln + 7lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -41ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-41 + 7x) = 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 '(-41 + 7x)' equal to zero and attempt to solve: Simplifying -41 + 7x = 0 Solving -41 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '41' to each side of the equation. -41 + 41 + 7x = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 7x = 0 + 41 7x = 0 + 41 Combine like terms: 0 + 41 = 41 7x = 41 Add '-7x' to each side of the equation. 7x + -7x = 41 + -7x Combine like terms: 7x + -7x = 0 0 = 41 + -7x Simplifying 0 = 41 + -7x 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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