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Simplifying Ln(10 + -1x) + ln(-6 + -1x) = ln(-34 + -15x) (10 * nL + -1x * nL) + ln(-6 + -1x) = ln(-34 + -15x) (10nL + -1nxL) + ln(-6 + -1x) = ln(-34 + -15x) 10nL + -1nxL + (-6 * ln + -1x * ln) = ln(-34 + -15x) 10nL + -1nxL + (-6ln + -1lnx) = ln(-34 + -15x) Reorder the terms: -6ln + -1lnx + 10nL + -1nxL = ln(-34 + -15x) -6ln + -1lnx + 10nL + -1nxL = (-34 * ln + -15x * ln) -6ln + -1lnx + 10nL + -1nxL = (-34ln + -15lnx) Solving -6ln + -1lnx + 10nL + -1nxL = -34ln + -15lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '34ln' to each side of the equation. -6ln + -1lnx + 10nL + 34ln + -1nxL = -34ln + 34ln + -15lnx Reorder the terms: -6ln + 34ln + -1lnx + 10nL + -1nxL = -34ln + 34ln + -15lnx Combine like terms: -6ln + 34ln = 28ln 28ln + -1lnx + 10nL + -1nxL = -34ln + 34ln + -15lnx Combine like terms: -34ln + 34ln = 0 28ln + -1lnx + 10nL + -1nxL = 0 + -15lnx 28ln + -1lnx + 10nL + -1nxL = -15lnx Add '15lnx' to each side of the equation. 28ln + -1lnx + 10nL + 15lnx + -1nxL = -15lnx + 15lnx Reorder the terms: 28ln + -1lnx + 15lnx + 10nL + -1nxL = -15lnx + 15lnx Combine like terms: -1lnx + 15lnx = 14lnx 28ln + 14lnx + 10nL + -1nxL = -15lnx + 15lnx Combine like terms: -15lnx + 15lnx = 0 28ln + 14lnx + 10nL + -1nxL = 0 Add '-10nL' to each side of the equation. 28ln + 14lnx + 10nL + -10nL + -1nxL = 0 + -10nL Combine like terms: 10nL + -10nL = 0 28ln + 14lnx + 0 + -1nxL = 0 + -10nL 28ln + 14lnx + -1nxL = 0 + -10nL Remove the zero: 28ln + 14lnx + -1nxL = -10nL Add 'nxL' to each side of the equation. 28ln + 14lnx + -1nxL + nxL = -10nL + nxL Combine like terms: -1nxL + nxL = 0 28ln + 14lnx + 0 = -10nL + nxL 28ln + 14lnx = -10nL + nxL Reorder the terms: 28ln + 14lnx + 10nL + -1nxL = -10nL + 10nL + nxL + -1nxL Combine like terms: -10nL + 10nL = 0 28ln + 14lnx + 10nL + -1nxL = 0 + nxL + -1nxL 28ln + 14lnx + 10nL + -1nxL = nxL + -1nxL Combine like terms: nxL + -1nxL = 0 28ln + 14lnx + 10nL + -1nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(28l + 14lx + 10L + -1xL) = 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 '(28l + 14lx + 10L + -1xL)' equal to zero and attempt to solve: Simplifying 28l + 14lx + 10L + -1xL = 0 Reorder the terms: 10L + 28l + 14lx + -1xL = 0 Solving 10L + 28l + 14lx + -1xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-10L' to each side of the equation. 10L + 28l + 14lx + -10L + -1xL = 0 + -10L Reorder the terms: 10L + -10L + 28l + 14lx + -1xL = 0 + -10L Combine like terms: 10L + -10L = 0 0 + 28l + 14lx + -1xL = 0 + -10L 28l + 14lx + -1xL = 0 + -10L Remove the zero: 28l + 14lx + -1xL = -10L Add 'xL' to each side of the equation. 28l + 14lx + -1xL + xL = -10L + xL Combine like terms: -1xL + xL = 0 28l + 14lx + 0 = -10L + xL 28l + 14lx = -10L + xL 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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