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Simplifying ln(y) = ln(5x) + ln(10) Multiply ln * y lny = ln(5x) + ln(10) Remove parenthesis around (5x) lny = ln * 5x + ln(10) Reorder the terms for easier multiplication: lny = 5ln * x + ln(10) Multiply ln * x lny = 5lnx + ln(10) Reorder the terms for easier multiplication: lny = 5lnx + 10ln Reorder the terms: lny = 10ln + 5lnx Solving lny = 10ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. -10ln + lny = 10ln + -10ln + 5lnx Combine like terms: 10ln + -10ln = 0 -10ln + lny = 0 + 5lnx -10ln + lny = 5lnx Add '-5lnx' to each side of the equation. -10ln + -5lnx + lny = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -10ln + -5lnx + lny = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-10 + -5x + 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 '(-10 + -5x + y)' equal to zero and attempt to solve: Simplifying -10 + -5x + y = 0 Solving -10 + -5x + 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 + -5x + 10 + y = 0 + 10 Reorder the terms: -10 + 10 + -5x + y = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -5x + y = 0 + 10 -5x + y = 0 + 10 Combine like terms: 0 + 10 = 10 -5x + y = 10 Add '5x' to each side of the equation. -5x + 5x + y = 10 + 5x Combine like terms: -5x + 5x = 0 0 + y = 10 + 5x y = 10 + 5x Add '-1y' to each side of the equation. y + -1y = 10 + 5x + -1y Combine like terms: y + -1y = 0 0 = 10 + 5x + -1y Simplifying 0 = 10 + 5x + -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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