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Simplifying 2ln(x + 2) = ln(10x) Reorder the terms: 2ln(2 + x) = ln(10x) (2 * 2ln + x * 2ln) = ln(10x) (4ln + 2lnx) = ln(10x) Remove parenthesis around (10x) 4ln + 2lnx = ln * 10x Reorder the terms for easier multiplication: 4ln + 2lnx = 10ln * x Multiply ln * x 4ln + 2lnx = 10lnx Solving 4ln + 2lnx = 10lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10lnx' to each side of the equation. 4ln + 2lnx + -10lnx = 10lnx + -10lnx Combine like terms: 2lnx + -10lnx = -8lnx 4ln + -8lnx = 10lnx + -10lnx Combine like terms: 10lnx + -10lnx = 0 4ln + -8lnx = 0 Factor out the Greatest Common Factor (GCF), '4ln'. 4ln(1 + -2x) = 0 Ignore the factor 4.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 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Add '2x' to each side of the equation. -2x + 2x = -1 + 2x Combine like terms: -2x + 2x = 0 0 = -1 + 2x Simplifying 0 = -1 + 2x 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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