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Simplifying Lnx + ln(x + 6) = ln(5x + 12) Reorder the terms: nxL + ln(6 + x) = ln(5x + 12) nxL + (6 * ln + x * ln) = ln(5x + 12) nxL + (6ln + lnx) = ln(5x + 12) Reorder the terms: 6ln + lnx + nxL = ln(5x + 12) Reorder the terms: 6ln + lnx + nxL = ln(12 + 5x) 6ln + lnx + nxL = (12 * ln + 5x * ln) 6ln + lnx + nxL = (12ln + 5lnx) Solving 6ln + lnx + nxL = 12ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. 6ln + lnx + -12ln + nxL = 12ln + -12ln + 5lnx Reorder the terms: 6ln + -12ln + lnx + nxL = 12ln + -12ln + 5lnx Combine like terms: 6ln + -12ln = -6ln -6ln + lnx + nxL = 12ln + -12ln + 5lnx Combine like terms: 12ln + -12ln = 0 -6ln + lnx + nxL = 0 + 5lnx -6ln + lnx + nxL = 5lnx Add '-5lnx' to each side of the equation. -6ln + lnx + -5lnx + nxL = 5lnx + -5lnx Combine like terms: lnx + -5lnx = -4lnx -6ln + -4lnx + nxL = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -6ln + -4lnx + nxL = 0 Add '-1nxL' to each side of the equation. -6ln + -4lnx + nxL + -1nxL = 0 + -1nxL Combine like terms: nxL + -1nxL = 0 -6ln + -4lnx + 0 = 0 + -1nxL -6ln + -4lnx = 0 + -1nxL Remove the zero: -6ln + -4lnx = -1nxL Combine like terms: -1nxL + nxL = 0 -6ln + -4lnx + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-6l + -4lx + 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 '(-6l + -4lx + xL)' equal to zero and attempt to solve: Simplifying -6l + -4lx + xL = 0 Solving -6l + -4lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-1xL' to each side of the equation. -6l + -4lx + xL + -1xL = 0 + -1xL Combine like terms: xL + -1xL = 0 -6l + -4lx + 0 = 0 + -1xL -6l + -4lx = 0 + -1xL Remove the zero: -6l + -4lx = -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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