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Simplifying ln(x) + ln(x + -6) = Ln(10) Multiply ln * x lnx + ln(x + -6) = Ln(10) Reorder the terms: lnx + ln(-6 + x) = Ln(10) lnx + (-6 * ln + x * ln) = Ln(10) lnx + (-6ln + lnx) = Ln(10) Reorder the terms: -6ln + lnx + lnx = Ln(10) Combine like terms: lnx + lnx = 2lnx -6ln + 2lnx = Ln(10) Reorder the terms for easier multiplication: -6ln + 2lnx = 10nL Solving -6ln + 2lnx = 10nL Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Combine like terms: 10nL + -10nL = 0 -6ln + 2lnx + -10nL = 0 Factor out the Greatest Common Factor (GCF), '2n'. 2n(-3l + lx + -5L) = 0 Ignore the factor 2.Subproblem 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 '(-3l + lx + -5L)' equal to zero and attempt to solve: Simplifying -3l + lx + -5L = 0 Reorder the terms: -5L + -3l + lx = 0 Solving -5L + -3l + lx = 0 Move all terms containing l to the left, all other terms to the right. Add '5L' to each side of the equation. -5L + -3l + 5L + lx = 0 + 5L Reorder the terms: -5L + 5L + -3l + lx = 0 + 5L Combine like terms: -5L + 5L = 0 0 + -3l + lx = 0 + 5L -3l + lx = 0 + 5L Remove the zero: -3l + lx = 5L 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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