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Simplifying 5ln(x) + -3ln(6x + y3) = ln(m) Multiply ln * x 5lnx + -3ln(6x + y3) = ln(m) 5lnx + (6x * -3ln + y3 * -3ln) = ln(m) 5lnx + (-18lnx + -3lny3) = ln(m) Combine like terms: 5lnx + -18lnx = -13lnx -13lnx + -3lny3 = ln(m) Multiply ln * m -13lnx + -3lny3 = lmn Solving -13lnx + -3lny3 = lmn Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lmn' to each side of the equation. -13lnx + -1lmn + -3lny3 = lmn + -1lmn Reorder the terms: -1lmn + -13lnx + -3lny3 = lmn + -1lmn Combine like terms: lmn + -1lmn = 0 -1lmn + -13lnx + -3lny3 = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(m + 13x + 3y3) = 0 Ignore the factor -1.Subproblem 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 '(m + 13x + 3y3)' equal to zero and attempt to solve: Simplifying m + 13x + 3y3 = 0 Solving m + 13x + 3y3 = 0 Move all terms containing l to the left, all other terms to the right. Add '-1m' to each side of the equation. m + 13x + -1m + 3y3 = 0 + -1m Reorder the terms: m + -1m + 13x + 3y3 = 0 + -1m Combine like terms: m + -1m = 0 0 + 13x + 3y3 = 0 + -1m 13x + 3y3 = 0 + -1m Remove the zero: 13x + 3y3 = -1m Add '-13x' to each side of the equation. 13x + -13x + 3y3 = -1m + -13x Combine like terms: 13x + -13x = 0 0 + 3y3 = -1m + -13x 3y3 = -1m + -13x Add '-3y3' to each side of the equation. 3y3 + -3y3 = -1m + -13x + -3y3 Combine like terms: 3y3 + -3y3 = 0 0 = -1m + -13x + -3y3 Simplifying 0 = -1m + -13x + -3y3 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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