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Simplifying Ln(2x + 5) + -1ln(6x + 1) = ln * 6 Reorder the terms: nL(5 + 2x) + -1ln(6x + 1) = ln * 6 (5 * nL + 2x * nL) + -1ln(6x + 1) = ln * 6 (5nL + 2nxL) + -1ln(6x + 1) = ln * 6 Reorder the terms: 5nL + 2nxL + -1ln(1 + 6x) = ln * 6 5nL + 2nxL + (1 * -1ln + 6x * -1ln) = ln * 6 5nL + 2nxL + (-1ln + -6lnx) = ln * 6 Reorder the terms: -1ln + -6lnx + 5nL + 2nxL = ln * 6 Reorder the terms for easier multiplication: -1ln + -6lnx + 5nL + 2nxL = 6ln Solving -1ln + -6lnx + 5nL + 2nxL = 6ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. -1ln + -6lnx + 5nL + -6ln + 2nxL = 6ln + -6ln Reorder the terms: -1ln + -6ln + -6lnx + 5nL + 2nxL = 6ln + -6ln Combine like terms: -1ln + -6ln = -7ln -7ln + -6lnx + 5nL + 2nxL = 6ln + -6ln Combine like terms: 6ln + -6ln = 0 -7ln + -6lnx + 5nL + 2nxL = 0 Add '-5nL' to each side of the equation. -7ln + -6lnx + 5nL + -5nL + 2nxL = 0 + -5nL Combine like terms: 5nL + -5nL = 0 -7ln + -6lnx + 0 + 2nxL = 0 + -5nL -7ln + -6lnx + 2nxL = 0 + -5nL Remove the zero: -7ln + -6lnx + 2nxL = -5nL Add '-2nxL' to each side of the equation. -7ln + -6lnx + 2nxL + -2nxL = -5nL + -2nxL Combine like terms: 2nxL + -2nxL = 0 -7ln + -6lnx + 0 = -5nL + -2nxL -7ln + -6lnx = -5nL + -2nxL Reorder the terms: -7ln + -6lnx + 5nL + 2nxL = -5nL + 5nL + -2nxL + 2nxL Combine like terms: -5nL + 5nL = 0 -7ln + -6lnx + 5nL + 2nxL = 0 + -2nxL + 2nxL -7ln + -6lnx + 5nL + 2nxL = -2nxL + 2nxL Combine like terms: -2nxL + 2nxL = 0 -7ln + -6lnx + 5nL + 2nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-7l + -6lx + 5L + 2xL) = 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 '(-7l + -6lx + 5L + 2xL)' equal to zero and attempt to solve: Simplifying -7l + -6lx + 5L + 2xL = 0 Reorder the terms: 5L + -7l + -6lx + 2xL = 0 Solving 5L + -7l + -6lx + 2xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-5L' to each side of the equation. 5L + -7l + -6lx + -5L + 2xL = 0 + -5L Reorder the terms: 5L + -5L + -7l + -6lx + 2xL = 0 + -5L Combine like terms: 5L + -5L = 0 0 + -7l + -6lx + 2xL = 0 + -5L -7l + -6lx + 2xL = 0 + -5L Remove the zero: -7l + -6lx + 2xL = -5L Add '-2xL' to each side of the equation. -7l + -6lx + 2xL + -2xL = -5L + -2xL Combine like terms: 2xL + -2xL = 0 -7l + -6lx + 0 = -5L + -2xL -7l + -6lx = -5L + -2xL 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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