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