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Simplifying Ln(x + -1) + ln(x + -4) = ln(10) Reorder the terms: nL(-1 + x) + ln(x + -4) = ln(10) (-1 * nL + x * nL) + ln(x + -4) = ln(10) (-1nL + nxL) + ln(x + -4) = ln(10) Reorder the terms: -1nL + nxL + ln(-4 + x) = ln(10) -1nL + nxL + (-4 * ln + x * ln) = ln(10) -1nL + nxL + (-4ln + lnx) = ln(10) Reorder the terms: -4ln + lnx + -1nL + nxL = ln(10) Reorder the terms for easier multiplication: -4ln + lnx + -1nL + nxL = 10ln Solving -4ln + lnx + -1nL + nxL = 10ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. -4ln + lnx + -1nL + -10ln + nxL = 10ln + -10ln Reorder the terms: -4ln + -10ln + lnx + -1nL + nxL = 10ln + -10ln Combine like terms: -4ln + -10ln = -14ln -14ln + lnx + -1nL + nxL = 10ln + -10ln Combine like terms: 10ln + -10ln = 0 -14ln + lnx + -1nL + nxL = 0 Add 'nL' to each side of the equation. -14ln + lnx + -1nL + nL + nxL = 0 + nL Combine like terms: -1nL + nL = 0 -14ln + lnx + 0 + nxL = 0 + nL -14ln + lnx + nxL = 0 + nL Remove the zero: -14ln + lnx + nxL = nL Add '-1nxL' to each side of the equation. -14ln + lnx + nxL + -1nxL = nL + -1nxL Combine like terms: nxL + -1nxL = 0 -14ln + lnx + 0 = nL + -1nxL -14ln + lnx = nL + -1nxL Reorder the terms: -14ln + lnx + -1nL + nxL = nL + -1nL + -1nxL + nxL Combine like terms: nL + -1nL = 0 -14ln + lnx + -1nL + nxL = 0 + -1nxL + nxL -14ln + lnx + -1nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 -14ln + lnx + -1nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-14l + lx + -1L + 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 '(-14l + lx + -1L + xL)' equal to zero and attempt to solve: Simplifying -14l + lx + -1L + xL = 0 Reorder the terms: -1L + -14l + lx + xL = 0 Solving -1L + -14l + lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add 'L' to each side of the equation. -1L + -14l + lx + L + xL = 0 + L Reorder the terms: -1L + L + -14l + lx + xL = 0 + L Combine like terms: -1L + L = 0 0 + -14l + lx + xL = 0 + L -14l + lx + xL = 0 + L Remove the zero: -14l + lx + xL = L Add '-1xL' to each side of the equation. -14l + lx + xL + -1xL = L + -1xL Combine like terms: xL + -1xL = 0 -14l + lx + 0 = L + -1xL -14l + lx = L + -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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