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Simplifying 12ln(x) + -1ln(x10) = ln(x + 30) Multiply ln * x 12lnx + -1ln(x10) = ln(x + 30) Multiply ln * x10 12lnx + -1lnx10 = ln(x + 30) Reorder the terms: 12lnx + -1lnx10 = ln(30 + x) 12lnx + -1lnx10 = (30 * ln + x * ln) 12lnx + -1lnx10 = (30ln + lnx) Solving 12lnx + -1lnx10 = 30ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-30ln' to each side of the equation. 12lnx + -30ln + -1lnx10 = 30ln + -30ln + lnx Reorder the terms: -30ln + 12lnx + -1lnx10 = 30ln + -30ln + lnx Combine like terms: 30ln + -30ln = 0 -30ln + 12lnx + -1lnx10 = 0 + lnx -30ln + 12lnx + -1lnx10 = lnx Add '-1lnx' to each side of the equation. -30ln + 12lnx + -1lnx + -1lnx10 = lnx + -1lnx Combine like terms: 12lnx + -1lnx = 11lnx -30ln + 11lnx + -1lnx10 = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -30ln + 11lnx + -1lnx10 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-30 + 11x + -1x10) = 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 '(-30 + 11x + -1x10)' equal to zero and attempt to solve: Simplifying -30 + 11x + -1x10 = 0 Solving -30 + 11x + -1x10 = 0 Move all terms containing l to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 11x + 30 + -1x10 = 0 + 30 Reorder the terms: -30 + 30 + 11x + -1x10 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 11x + -1x10 = 0 + 30 11x + -1x10 = 0 + 30 Combine like terms: 0 + 30 = 30 11x + -1x10 = 30 Add '-11x' to each side of the equation. 11x + -11x + -1x10 = 30 + -11x Combine like terms: 11x + -11x = 0 0 + -1x10 = 30 + -11x -1x10 = 30 + -11x Add 'x10' to each side of the equation. -1x10 + x10 = 30 + -11x + x10 Combine like terms: -1x10 + x10 = 0 0 = 30 + -11x + x10 Simplifying 0 = 30 + -11x + x10 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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