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Simplifying Ln(3x + -1) + ln(x + -5) = ln * 5 Reorder the terms: nL(-1 + 3x) + ln(x + -5) = ln * 5 (-1 * nL + 3x * nL) + ln(x + -5) = ln * 5 (-1nL + 3nxL) + ln(x + -5) = ln * 5 Reorder the terms: -1nL + 3nxL + ln(-5 + x) = ln * 5 -1nL + 3nxL + (-5 * ln + x * ln) = ln * 5 -1nL + 3nxL + (-5ln + lnx) = ln * 5 Reorder the terms: -5ln + lnx + -1nL + 3nxL = ln * 5 Reorder the terms for easier multiplication: -5ln + lnx + -1nL + 3nxL = 5ln Solving -5ln + lnx + -1nL + 3nxL = 5ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. -5ln + lnx + -1nL + -5ln + 3nxL = 5ln + -5ln Reorder the terms: -5ln + -5ln + lnx + -1nL + 3nxL = 5ln + -5ln Combine like terms: -5ln + -5ln = -10ln -10ln + lnx + -1nL + 3nxL = 5ln + -5ln Combine like terms: 5ln + -5ln = 0 -10ln + lnx + -1nL + 3nxL = 0 Add 'nL' to each side of the equation. -10ln + lnx + -1nL + nL + 3nxL = 0 + nL Combine like terms: -1nL + nL = 0 -10ln + lnx + 0 + 3nxL = 0 + nL -10ln + lnx + 3nxL = 0 + nL Remove the zero: -10ln + lnx + 3nxL = nL Add '-3nxL' to each side of the equation. -10ln + lnx + 3nxL + -3nxL = nL + -3nxL Combine like terms: 3nxL + -3nxL = 0 -10ln + lnx + 0 = nL + -3nxL -10ln + lnx = nL + -3nxL Reorder the terms: -10ln + lnx + -1nL + 3nxL = nL + -1nL + -3nxL + 3nxL Combine like terms: nL + -1nL = 0 -10ln + lnx + -1nL + 3nxL = 0 + -3nxL + 3nxL -10ln + lnx + -1nL + 3nxL = -3nxL + 3nxL Combine like terms: -3nxL + 3nxL = 0 -10ln + lnx + -1nL + 3nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-10l + lx + -1L + 3xL) = 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 '(-10l + lx + -1L + 3xL)' equal to zero and attempt to solve: Simplifying -10l + lx + -1L + 3xL = 0 Reorder the terms: -1L + -10l + lx + 3xL = 0 Solving -1L + -10l + lx + 3xL = 0 Move all terms containing l to the left, all other terms to the right. Add 'L' to each side of the equation. -1L + -10l + lx + L + 3xL = 0 + L Reorder the terms: -1L + L + -10l + lx + 3xL = 0 + L Combine like terms: -1L + L = 0 0 + -10l + lx + 3xL = 0 + L -10l + lx + 3xL = 0 + L Remove the zero: -10l + lx + 3xL = L Add '-3xL' to each side of the equation. -10l + lx + 3xL + -3xL = L + -3xL Combine like terms: 3xL + -3xL = 0 -10l + lx + 0 = L + -3xL -10l + lx = L + -3xL 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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