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Simplifying ln(6x + -13) = ln(2x + 15) Reorder the terms: ln(-13 + 6x) = ln(2x + 15) (-13 * ln + 6x * ln) = ln(2x + 15) (-13ln + 6lnx) = ln(2x + 15) Reorder the terms: -13ln + 6lnx = ln(15 + 2x) -13ln + 6lnx = (15 * ln + 2x * ln) -13ln + 6lnx = (15ln + 2lnx) Solving -13ln + 6lnx = 15ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-15ln' to each side of the equation. -13ln + -15ln + 6lnx = 15ln + -15ln + 2lnx Combine like terms: -13ln + -15ln = -28ln -28ln + 6lnx = 15ln + -15ln + 2lnx Combine like terms: 15ln + -15ln = 0 -28ln + 6lnx = 0 + 2lnx -28ln + 6lnx = 2lnx Add '-2lnx' to each side of the equation. -28ln + 6lnx + -2lnx = 2lnx + -2lnx Combine like terms: 6lnx + -2lnx = 4lnx -28ln + 4lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -28ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), '4ln'. 4ln(-7 + x) = 0 Ignore the factor 4.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 '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 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 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Add '-1x' to each side of the equation. x + -1x = 7 + -1x Combine like terms: x + -1x = 0 0 = 7 + -1x Simplifying 0 = 7 + -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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