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Simplifying ln(x + 2) + -1ln(5x) = 0 Reorder the terms: ln(2 + x) + -1ln(5x) = 0 (2 * ln + x * ln) + -1ln(5x) = 0 (2ln + lnx) + -1ln(5x) = 0 Remove parenthesis around (5x) 2ln + lnx + -1ln * 5x = 0 Reorder the terms for easier multiplication: 2ln + lnx + -1 * 5ln * x = 0 Multiply -1 * 5 2ln + lnx + -5ln * x = 0 Multiply ln * x 2ln + lnx + -5lnx = 0 Combine like terms: lnx + -5lnx = -4lnx 2ln + -4lnx = 0 Solving 2ln + -4lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(1 + -2x) = 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 + -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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