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Simplifying Ln(x + -5) + ln(x + 2) = ln(18) Reorder the terms: nL(-5 + x) + ln(x + 2) = ln(18) (-5 * nL + x * nL) + ln(x + 2) = ln(18) (-5nL + nxL) + ln(x + 2) = ln(18) Reorder the terms: -5nL + nxL + ln(2 + x) = ln(18) -5nL + nxL + (2 * ln + x * ln) = ln(18) -5nL + nxL + (2ln + lnx) = ln(18) Reorder the terms: 2ln + lnx + -5nL + nxL = ln(18) Reorder the terms for easier multiplication: 2ln + lnx + -5nL + nxL = 18ln Solving 2ln + lnx + -5nL + nxL = 18ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-18ln' to each side of the equation. 2ln + lnx + -5nL + -18ln + nxL = 18ln + -18ln Reorder the terms: 2ln + -18ln + lnx + -5nL + nxL = 18ln + -18ln Combine like terms: 2ln + -18ln = -16ln -16ln + lnx + -5nL + nxL = 18ln + -18ln Combine like terms: 18ln + -18ln = 0 -16ln + lnx + -5nL + nxL = 0 Add '5nL' to each side of the equation. -16ln + lnx + -5nL + 5nL + nxL = 0 + 5nL Combine like terms: -5nL + 5nL = 0 -16ln + lnx + 0 + nxL = 0 + 5nL -16ln + lnx + nxL = 0 + 5nL Remove the zero: -16ln + lnx + nxL = 5nL Add '-1nxL' to each side of the equation. -16ln + lnx + nxL + -1nxL = 5nL + -1nxL Combine like terms: nxL + -1nxL = 0 -16ln + lnx + 0 = 5nL + -1nxL -16ln + lnx = 5nL + -1nxL Reorder the terms: -16ln + lnx + -5nL + nxL = 5nL + -5nL + -1nxL + nxL Combine like terms: 5nL + -5nL = 0 -16ln + lnx + -5nL + nxL = 0 + -1nxL + nxL -16ln + lnx + -5nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 -16ln + lnx + -5nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-16l + lx + -5L + 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 '(-16l + lx + -5L + xL)' equal to zero and attempt to solve: Simplifying -16l + lx + -5L + xL = 0 Reorder the terms: -5L + -16l + lx + xL = 0 Solving -5L + -16l + lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '5L' to each side of the equation. -5L + -16l + lx + 5L + xL = 0 + 5L Reorder the terms: -5L + 5L + -16l + lx + xL = 0 + 5L Combine like terms: -5L + 5L = 0 0 + -16l + lx + xL = 0 + 5L -16l + lx + xL = 0 + 5L Remove the zero: -16l + lx + xL = 5L Add '-1xL' to each side of the equation. -16l + lx + xL + -1xL = 5L + -1xL Combine like terms: xL + -1xL = 0 -16l + lx + 0 = 5L + -1xL -16l + lx = 5L + -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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