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Simplifying ln(y) = ln(x) + ln(x + 10) + ln(c) Multiply ln * y lny = ln(x) + ln(x + 10) + ln(c) Multiply ln * x lny = lnx + ln(x + 10) + ln(c) Reorder the terms: lny = lnx + ln(10 + x) + ln(c) lny = lnx + (10 * ln + x * ln) + ln(c) lny = lnx + (10ln + lnx) + ln(c) Multiply ln * c lny = lnx + 10ln + lnx + cln Reorder the terms: lny = cln + 10ln + lnx + lnx Combine like terms: lnx + lnx = 2lnx lny = cln + 10ln + 2lnx Solving lny = cln + 10ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1cln' to each side of the equation. -1cln + lny = cln + 10ln + -1cln + 2lnx Reorder the terms: -1cln + lny = cln + -1cln + 10ln + 2lnx Combine like terms: cln + -1cln = 0 -1cln + lny = 0 + 10ln + 2lnx -1cln + lny = 10ln + 2lnx Add '-10ln' to each side of the equation. -1cln + -10ln + lny = 10ln + -10ln + 2lnx Combine like terms: 10ln + -10ln = 0 -1cln + -10ln + lny = 0 + 2lnx -1cln + -10ln + lny = 2lnx Add '-2lnx' to each side of the equation. -1cln + -10ln + -2lnx + lny = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -1cln + -10ln + -2lnx + lny = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-1c + -10 + -2x + y) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 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 '(-1c + -10 + -2x + y)' equal to zero and attempt to solve: Simplifying -1c + -10 + -2x + y = 0 Reorder the terms: -10 + -1c + -2x + y = 0 Solving -10 + -1c + -2x + y = 0 Move all terms containing l to the left, all other terms to the right. Add '10' to each side of the equation. -10 + -1c + -2x + 10 + y = 0 + 10 Reorder the terms: -10 + 10 + -1c + -2x + y = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1c + -2x + y = 0 + 10 -1c + -2x + y = 0 + 10 Combine like terms: 0 + 10 = 10 -1c + -2x + y = 10 Add 'c' to each side of the equation. -1c + -2x + c + y = 10 + c Reorder the terms: -1c + c + -2x + y = 10 + c Combine like terms: -1c + c = 0 0 + -2x + y = 10 + c -2x + y = 10 + c Add '2x' to each side of the equation. -2x + 2x + y = 10 + c + 2x Combine like terms: -2x + 2x = 0 0 + y = 10 + c + 2x y = 10 + c + 2x Add '-1y' to each side of the equation. y + -1y = 10 + c + 2x + -1y Combine like terms: y + -1y = 0 0 = 10 + c + 2x + -1y Simplifying 0 = 10 + c + 2x + -1y 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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