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Simplifying Ln(4x + -7) + ln(x + -5) = 2lnx Reorder the terms: nL(-7 + 4x) + ln(x + -5) = 2lnx (-7 * nL + 4x * nL) + ln(x + -5) = 2lnx (-7nL + 4nxL) + ln(x + -5) = 2lnx Reorder the terms: -7nL + 4nxL + ln(-5 + x) = 2lnx -7nL + 4nxL + (-5 * ln + x * ln) = 2lnx -7nL + 4nxL + (-5ln + lnx) = 2lnx Reorder the terms: -5ln + lnx + -7nL + 4nxL = 2lnx Solving -5ln + lnx + -7nL + 4nxL = 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2lnx' to each side of the equation. -5ln + lnx + -7nL + -2lnx + 4nxL = 2lnx + -2lnx Reorder the terms: -5ln + lnx + -2lnx + -7nL + 4nxL = 2lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx -5ln + -1lnx + -7nL + 4nxL = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -5ln + -1lnx + -7nL + 4nxL = 0 Add '7nL' to each side of the equation. -5ln + -1lnx + -7nL + 7nL + 4nxL = 0 + 7nL Combine like terms: -7nL + 7nL = 0 -5ln + -1lnx + 0 + 4nxL = 0 + 7nL -5ln + -1lnx + 4nxL = 0 + 7nL Remove the zero: -5ln + -1lnx + 4nxL = 7nL Add '-4nxL' to each side of the equation. -5ln + -1lnx + 4nxL + -4nxL = 7nL + -4nxL Combine like terms: 4nxL + -4nxL = 0 -5ln + -1lnx + 0 = 7nL + -4nxL -5ln + -1lnx = 7nL + -4nxL Reorder the terms: -5ln + -1lnx + -7nL + 4nxL = 7nL + -7nL + -4nxL + 4nxL Combine like terms: 7nL + -7nL = 0 -5ln + -1lnx + -7nL + 4nxL = 0 + -4nxL + 4nxL -5ln + -1lnx + -7nL + 4nxL = -4nxL + 4nxL Combine like terms: -4nxL + 4nxL = 0 -5ln + -1lnx + -7nL + 4nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-5l + -1lx + -7L + 4xL) = 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 + -1lx + -7L + 4xL)' equal to zero and attempt to solve: Simplifying -5l + -1lx + -7L + 4xL = 0 Reorder the terms: -7L + -5l + -1lx + 4xL = 0 Solving -7L + -5l + -1lx + 4xL = 0 Move all terms containing l to the left, all other terms to the right. Add '7L' to each side of the equation. -7L + -5l + -1lx + 7L + 4xL = 0 + 7L Reorder the terms: -7L + 7L + -5l + -1lx + 4xL = 0 + 7L Combine like terms: -7L + 7L = 0 0 + -5l + -1lx + 4xL = 0 + 7L -5l + -1lx + 4xL = 0 + 7L Remove the zero: -5l + -1lx + 4xL = 7L Add '-4xL' to each side of the equation. -5l + -1lx + 4xL + -4xL = 7L + -4xL Combine like terms: 4xL + -4xL = 0 -5l + -1lx + 0 = 7L + -4xL -5l + -1lx = 7L + -4xL 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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