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Simplifying ln(5x) = ln(3x + 10) Remove parenthesis around (5x) ln * 5x = ln(3x + 10) Reorder the terms for easier multiplication: 5ln * x = ln(3x + 10) Multiply ln * x 5lnx = ln(3x + 10) Reorder the terms: 5lnx = ln(10 + 3x) 5lnx = (10 * ln + 3x * ln) 5lnx = (10ln + 3lnx) Solving 5lnx = 10ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. -10ln + 5lnx = 10ln + -10ln + 3lnx Combine like terms: 10ln + -10ln = 0 -10ln + 5lnx = 0 + 3lnx -10ln + 5lnx = 3lnx Add '-3lnx' to each side of the equation. -10ln + 5lnx + -3lnx = 3lnx + -3lnx Combine like terms: 5lnx + -3lnx = 2lnx -10ln + 2lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -10ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-5 + x) = 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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Add '-1x' to each side of the equation. x + -1x = 5 + -1x Combine like terms: x + -1x = 0 0 = 5 + -1x Simplifying 0 = 5 + -1x 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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