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Simplifying ln(7x + -13) = ln(2x + 17) Reorder the terms: ln(-13 + 7x) = ln(2x + 17) (-13 * ln + 7x * ln) = ln(2x + 17) (-13ln + 7lnx) = ln(2x + 17) Reorder the terms: -13ln + 7lnx = ln(17 + 2x) -13ln + 7lnx = (17 * ln + 2x * ln) -13ln + 7lnx = (17ln + 2lnx) Solving -13ln + 7lnx = 17ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-17ln' to each side of the equation. -13ln + -17ln + 7lnx = 17ln + -17ln + 2lnx Combine like terms: -13ln + -17ln = -30ln -30ln + 7lnx = 17ln + -17ln + 2lnx Combine like terms: 17ln + -17ln = 0 -30ln + 7lnx = 0 + 2lnx -30ln + 7lnx = 2lnx Add '-2lnx' to each side of the equation. -30ln + 7lnx + -2lnx = 2lnx + -2lnx Combine like terms: 7lnx + -2lnx = 5lnx -30ln + 5lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -30ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(-6 + x) = 0 Ignore the factor 5.Subproblem 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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Add '-1x' to each side of the equation. x + -1x = 6 + -1x Combine like terms: x + -1x = 0 0 = 6 + -1x Simplifying 0 = 6 + -1x 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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