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