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Simplifying ln(2x + 1) = ln(7x + -10) Reorder the terms: ln(1 + 2x) = ln(7x + -10) (1 * ln + 2x * ln) = ln(7x + -10) (1ln + 2lnx) = ln(7x + -10) Reorder the terms: 1ln + 2lnx = ln(-10 + 7x) 1ln + 2lnx = (-10 * ln + 7x * ln) 1ln + 2lnx = (-10ln + 7lnx) Solving 1ln + 2lnx = -10ln + 7lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '10ln' to each side of the equation. 1ln + 10ln + 2lnx = -10ln + 10ln + 7lnx Combine like terms: 1ln + 10ln = 11ln 11ln + 2lnx = -10ln + 10ln + 7lnx Combine like terms: -10ln + 10ln = 0 11ln + 2lnx = 0 + 7lnx 11ln + 2lnx = 7lnx Add '-7lnx' to each side of the equation. 11ln + 2lnx + -7lnx = 7lnx + -7lnx Combine like terms: 2lnx + -7lnx = -5lnx 11ln + -5lnx = 7lnx + -7lnx Combine like terms: 7lnx + -7lnx = 0 11ln + -5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(11 + -5x) = 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 '(11 + -5x)' equal to zero and attempt to solve: Simplifying 11 + -5x = 0 Solving 11 + -5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -5x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -5x = 0 + -11 -5x = 0 + -11 Combine like terms: 0 + -11 = -11 -5x = -11 Add '5x' to each side of the equation. -5x + 5x = -11 + 5x Combine like terms: -5x + 5x = 0 0 = -11 + 5x Simplifying 0 = -11 + 5x 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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