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Simplifying Ln(x + 12) + -1lnx = ln(x + 5) Reorder the terms: nL(12 + x) + -1lnx = ln(x + 5) (12 * nL + x * nL) + -1lnx = ln(x + 5) (12nL + nxL) + -1lnx = ln(x + 5) Reorder the terms: -1lnx + 12nL + nxL = ln(x + 5) Reorder the terms: -1lnx + 12nL + nxL = ln(5 + x) -1lnx + 12nL + nxL = (5 * ln + x * ln) -1lnx + 12nL + nxL = (5ln + lnx) Solving -1lnx + 12nL + nxL = 5ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. -1lnx + 12nL + -5ln + nxL = 5ln + -5ln + lnx Reorder the terms: -5ln + -1lnx + 12nL + nxL = 5ln + -5ln + lnx Combine like terms: 5ln + -5ln = 0 -5ln + -1lnx + 12nL + nxL = 0 + lnx -5ln + -1lnx + 12nL + nxL = lnx Add '-1lnx' to each side of the equation. -5ln + -1lnx + 12nL + -1lnx + nxL = lnx + -1lnx Reorder the terms: -5ln + -1lnx + -1lnx + 12nL + nxL = lnx + -1lnx Combine like terms: -1lnx + -1lnx = -2lnx -5ln + -2lnx + 12nL + nxL = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -5ln + -2lnx + 12nL + nxL = 0 Add '-12nL' to each side of the equation. -5ln + -2lnx + 12nL + -12nL + nxL = 0 + -12nL Combine like terms: 12nL + -12nL = 0 -5ln + -2lnx + 0 + nxL = 0 + -12nL -5ln + -2lnx + nxL = 0 + -12nL Remove the zero: -5ln + -2lnx + nxL = -12nL Add '-1nxL' to each side of the equation. -5ln + -2lnx + nxL + -1nxL = -12nL + -1nxL Combine like terms: nxL + -1nxL = 0 -5ln + -2lnx + 0 = -12nL + -1nxL -5ln + -2lnx = -12nL + -1nxL Reorder the terms: -5ln + -2lnx + 12nL + nxL = -12nL + 12nL + -1nxL + nxL Combine like terms: -12nL + 12nL = 0 -5ln + -2lnx + 12nL + nxL = 0 + -1nxL + nxL -5ln + -2lnx + 12nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 -5ln + -2lnx + 12nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-5l + -2lx + 12L + 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 '(-5l + -2lx + 12L + xL)' equal to zero and attempt to solve: Simplifying -5l + -2lx + 12L + xL = 0 Reorder the terms: 12L + -5l + -2lx + xL = 0 Solving 12L + -5l + -2lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-12L' to each side of the equation. 12L + -5l + -2lx + -12L + xL = 0 + -12L Reorder the terms: 12L + -12L + -5l + -2lx + xL = 0 + -12L Combine like terms: 12L + -12L = 0 0 + -5l + -2lx + xL = 0 + -12L -5l + -2lx + xL = 0 + -12L Remove the zero: -5l + -2lx + xL = -12L Add '-1xL' to each side of the equation. -5l + -2lx + xL + -1xL = -12L + -1xL Combine like terms: xL + -1xL = 0 -5l + -2lx + 0 = -12L + -1xL -5l + -2lx = -12L + -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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