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Simplifying ln(5x + -19) = ln(2x + 11) Reorder the terms: ln(-19 + 5x) = ln(2x + 11) (-19 * ln + 5x * ln) = ln(2x + 11) (-19ln + 5lnx) = ln(2x + 11) Reorder the terms: -19ln + 5lnx = ln(11 + 2x) -19ln + 5lnx = (11 * ln + 2x * ln) -19ln + 5lnx = (11ln + 2lnx) Solving -19ln + 5lnx = 11ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-11ln' to each side of the equation. -19ln + -11ln + 5lnx = 11ln + -11ln + 2lnx Combine like terms: -19ln + -11ln = -30ln -30ln + 5lnx = 11ln + -11ln + 2lnx Combine like terms: 11ln + -11ln = 0 -30ln + 5lnx = 0 + 2lnx -30ln + 5lnx = 2lnx Add '-2lnx' to each side of the equation. -30ln + 5lnx + -2lnx = 2lnx + -2lnx Combine like terms: 5lnx + -2lnx = 3lnx -30ln + 3lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -30ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-10 + x) = 0 Ignore the factor 3.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 '(-10 + x)' equal to zero and attempt to solve: Simplifying -10 + x = 0 Solving -10 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0 + 10 x = 0 + 10 Combine like terms: 0 + 10 = 10 x = 10 Add '-1x' to each side of the equation. x + -1x = 10 + -1x Combine like terms: x + -1x = 0 0 = 10 + -1x Simplifying 0 = 10 + -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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