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Simplifying ln(x + -3) + ln(x + -4) = Ln(7 + -1x) Reorder the terms: ln(-3 + x) + ln(x + -4) = Ln(7 + -1x) (-3 * ln + x * ln) + ln(x + -4) = Ln(7 + -1x) (-3ln + lnx) + ln(x + -4) = Ln(7 + -1x) Reorder the terms: -3ln + lnx + ln(-4 + x) = Ln(7 + -1x) -3ln + lnx + (-4 * ln + x * ln) = Ln(7 + -1x) -3ln + lnx + (-4ln + lnx) = Ln(7 + -1x) Reorder the terms: -3ln + -4ln + lnx + lnx = Ln(7 + -1x) Combine like terms: -3ln + -4ln = -7ln -7ln + lnx + lnx = Ln(7 + -1x) Combine like terms: lnx + lnx = 2lnx -7ln + 2lnx = Ln(7 + -1x) -7ln + 2lnx = (7 * nL + -1x * nL) -7ln + 2lnx = (7nL + -1nxL) Solving -7ln + 2lnx = 7nL + -1nxL Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Reorder the terms: -7ln + 2lnx + -7nL + nxL = 7nL + -7nL + -1nxL + nxL Combine like terms: 7nL + -7nL = 0 -7ln + 2lnx + -7nL + nxL = 0 + -1nxL + nxL -7ln + 2lnx + -7nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 -7ln + 2lnx + -7nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-7l + 2lx + -7L + 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 '(-7l + 2lx + -7L + xL)' equal to zero and attempt to solve: Simplifying -7l + 2lx + -7L + xL = 0 Reorder the terms: -7L + -7l + 2lx + xL = 0 Solving -7L + -7l + 2lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '7L' to each side of the equation. -7L + -7l + 2lx + 7L + xL = 0 + 7L Reorder the terms: -7L + 7L + -7l + 2lx + xL = 0 + 7L Combine like terms: -7L + 7L = 0 0 + -7l + 2lx + xL = 0 + 7L -7l + 2lx + xL = 0 + 7L Remove the zero: -7l + 2lx + xL = 7L Add '-1xL' to each side of the equation. -7l + 2lx + xL + -1xL = 7L + -1xL Combine like terms: xL + -1xL = 0 -7l + 2lx + 0 = 7L + -1xL -7l + 2lx = 7L + -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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