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Simplifying Ln(x + 7) + ln(x + -1) = ln(4x + 1) Reorder the terms: nL(7 + x) + ln(x + -1) = ln(4x + 1) (7 * nL + x * nL) + ln(x + -1) = ln(4x + 1) (7nL + nxL) + ln(x + -1) = ln(4x + 1) Reorder the terms: 7nL + nxL + ln(-1 + x) = ln(4x + 1) 7nL + nxL + (-1 * ln + x * ln) = ln(4x + 1) 7nL + nxL + (-1ln + lnx) = ln(4x + 1) Reorder the terms: -1ln + lnx + 7nL + nxL = ln(4x + 1) Reorder the terms: -1ln + lnx + 7nL + nxL = ln(1 + 4x) -1ln + lnx + 7nL + nxL = (1 * ln + 4x * ln) -1ln + lnx + 7nL + nxL = (1ln + 4lnx) Solving -1ln + lnx + 7nL + nxL = 1ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. -1ln + lnx + 7nL + -1ln + nxL = 1ln + -1ln + 4lnx Reorder the terms: -1ln + -1ln + lnx + 7nL + nxL = 1ln + -1ln + 4lnx Combine like terms: -1ln + -1ln = -2ln -2ln + lnx + 7nL + nxL = 1ln + -1ln + 4lnx Combine like terms: 1ln + -1ln = 0 -2ln + lnx + 7nL + nxL = 0 + 4lnx -2ln + lnx + 7nL + nxL = 4lnx Add '-4lnx' to each side of the equation. -2ln + lnx + 7nL + -4lnx + nxL = 4lnx + -4lnx Reorder the terms: -2ln + lnx + -4lnx + 7nL + nxL = 4lnx + -4lnx Combine like terms: lnx + -4lnx = -3lnx -2ln + -3lnx + 7nL + nxL = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 -2ln + -3lnx + 7nL + nxL = 0 Add '-7nL' to each side of the equation. -2ln + -3lnx + 7nL + -7nL + nxL = 0 + -7nL Combine like terms: 7nL + -7nL = 0 -2ln + -3lnx + 0 + nxL = 0 + -7nL -2ln + -3lnx + nxL = 0 + -7nL Remove the zero: -2ln + -3lnx + nxL = -7nL Add '-1nxL' to each side of the equation. -2ln + -3lnx + nxL + -1nxL = -7nL + -1nxL Combine like terms: nxL + -1nxL = 0 -2ln + -3lnx + 0 = -7nL + -1nxL -2ln + -3lnx = -7nL + -1nxL Reorder the terms: -2ln + -3lnx + 7nL + nxL = -7nL + 7nL + -1nxL + nxL Combine like terms: -7nL + 7nL = 0 -2ln + -3lnx + 7nL + nxL = 0 + -1nxL + nxL -2ln + -3lnx + 7nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 -2ln + -3lnx + 7nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-2l + -3lx + 7L + 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 '(-2l + -3lx + 7L + xL)' equal to zero and attempt to solve: Simplifying -2l + -3lx + 7L + xL = 0 Reorder the terms: 7L + -2l + -3lx + xL = 0 Solving 7L + -2l + -3lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-7L' to each side of the equation. 7L + -2l + -3lx + -7L + xL = 0 + -7L Reorder the terms: 7L + -7L + -2l + -3lx + xL = 0 + -7L Combine like terms: 7L + -7L = 0 0 + -2l + -3lx + xL = 0 + -7L -2l + -3lx + xL = 0 + -7L Remove the zero: -2l + -3lx + xL = -7L Add '-1xL' to each side of the equation. -2l + -3lx + xL + -1xL = -7L + -1xL Combine like terms: xL + -1xL = 0 -2l + -3lx + 0 = -7L + -1xL -2l + -3lx = -7L + -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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