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Simplifying ln(10x + 2x) = 2ln(x + 1) Combine like terms: 10x + 2x = 12x ln(12x) = 2ln(x + 1) Remove parenthesis around (12x) ln * 12x = 2ln(x + 1) Reorder the terms for easier multiplication: 12ln * x = 2ln(x + 1) Multiply ln * x 12lnx = 2ln(x + 1) Reorder the terms: 12lnx = 2ln(1 + x) 12lnx = (1 * 2ln + x * 2ln) 12lnx = (2ln + 2lnx) Solving 12lnx = 2ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. -2ln + 12lnx = 2ln + -2ln + 2lnx Combine like terms: 2ln + -2ln = 0 -2ln + 12lnx = 0 + 2lnx -2ln + 12lnx = 2lnx Add '-2lnx' to each side of the equation. -2ln + 12lnx + -2lnx = 2lnx + -2lnx Combine like terms: 12lnx + -2lnx = 10lnx -2ln + 10lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -2ln + 10lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-1 + 5x) = 0 Ignore the factor 2.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 '(-1 + 5x)' equal to zero and attempt to solve: Simplifying -1 + 5x = 0 Solving -1 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 5x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 5x = 0 + 1 5x = 0 + 1 Combine like terms: 0 + 1 = 1 5x = 1 Add '-5x' to each side of the equation. 5x + -5x = 1 + -5x Combine like terms: 5x + -5x = 0 0 = 1 + -5x Simplifying 0 = 1 + -5x 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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