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Simplifying ln(5x + 1) = ln(x + 11) Reorder the terms: ln(1 + 5x) = ln(x + 11) (1 * ln + 5x * ln) = ln(x + 11) (1ln + 5lnx) = ln(x + 11) Reorder the terms: 1ln + 5lnx = ln(11 + x) 1ln + 5lnx = (11 * ln + x * ln) 1ln + 5lnx = (11ln + lnx) Solving 1ln + 5lnx = 11ln + lnx 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. 1ln + -11ln + 5lnx = 11ln + -11ln + lnx Combine like terms: 1ln + -11ln = -10ln -10ln + 5lnx = 11ln + -11ln + lnx Combine like terms: 11ln + -11ln = 0 -10ln + 5lnx = 0 + lnx -10ln + 5lnx = lnx Add '-1lnx' to each side of the equation. -10ln + 5lnx + -1lnx = lnx + -1lnx Combine like terms: 5lnx + -1lnx = 4lnx -10ln + 4lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -10ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-5 + 2x) = 0 Ignore the factor 2.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 '(-5 + 2x)' equal to zero and attempt to solve: Simplifying -5 + 2x = 0 Solving -5 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x = 0 + 5 2x = 0 + 5 Combine like terms: 0 + 5 = 5 2x = 5 Add '-2x' to each side of the equation. 2x + -2x = 5 + -2x Combine like terms: 2x + -2x = 0 0 = 5 + -2x Simplifying 0 = 5 + -2x 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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