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Simplifying Ln(x + 5) + ln(3x + 1) = 0 Reorder the terms: nL(5 + x) + ln(3x + 1) = 0 (5 * nL + x * nL) + ln(3x + 1) = 0 (5nL + nxL) + ln(3x + 1) = 0 Reorder the terms: 5nL + nxL + ln(1 + 3x) = 0 5nL + nxL + (1 * ln + 3x * ln) = 0 5nL + nxL + (1ln + 3lnx) = 0 Reorder the terms: 1ln + 3lnx + 5nL + nxL = 0 Solving 1ln + 3lnx + 5nL + nxL = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5nL' to each side of the equation. 1ln + 3lnx + 5nL + -5nL + nxL = 0 + -5nL Combine like terms: 5nL + -5nL = 0 1ln + 3lnx + 0 + nxL = 0 + -5nL 1ln + 3lnx + nxL = 0 + -5nL Remove the zero: 1ln + 3lnx + nxL = -5nL Add '-1nxL' to each side of the equation. 1ln + 3lnx + nxL + -1nxL = -5nL + -1nxL Combine like terms: nxL + -1nxL = 0 1ln + 3lnx + 0 = -5nL + -1nxL 1ln + 3lnx = -5nL + -1nxL Reorder the terms: 1ln + 3lnx + 5nL + nxL = -5nL + 5nL + -1nxL + nxL Combine like terms: -5nL + 5nL = 0 1ln + 3lnx + 5nL + nxL = 0 + -1nxL + nxL 1ln + 3lnx + 5nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 1ln + 3lnx + 5nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(l + 3lx + 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 '(l + 3lx + 5L + xL)' equal to zero and attempt to solve: Simplifying l + 3lx + 5L + xL = 0 Reorder the terms: 5L + l + 3lx + xL = 0 Solving 5L + l + 3lx + 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 + l + 3lx + -5L + xL = 0 + -5L Reorder the terms: 5L + -5L + l + 3lx + xL = 0 + -5L Combine like terms: 5L + -5L = 0 0 + l + 3lx + xL = 0 + -5L l + 3lx + xL = 0 + -5L Remove the zero: l + 3lx + xL = -5L Add '-1xL' to each side of the equation. l + 3lx + xL + -1xL = -5L + -1xL Combine like terms: xL + -1xL = 0 l + 3lx + 0 = -5L + -1xL l + 3lx = -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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