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Simplifying ln(2x) = ln(3x) + ln(4x + 5) Remove parenthesis around (2x) ln * 2x = ln(3x) + ln(4x + 5) Reorder the terms for easier multiplication: 2ln * x = ln(3x) + ln(4x + 5) Multiply ln * x 2lnx = ln(3x) + ln(4x + 5) Remove parenthesis around (3x) 2lnx = ln * 3x + ln(4x + 5) Reorder the terms for easier multiplication: 2lnx = 3ln * x + ln(4x + 5) Multiply ln * x 2lnx = 3lnx + ln(4x + 5) Reorder the terms: 2lnx = 3lnx + ln(5 + 4x) 2lnx = 3lnx + (5 * ln + 4x * ln) 2lnx = 3lnx + (5ln + 4lnx) Reorder the terms: 2lnx = 5ln + 3lnx + 4lnx Combine like terms: 3lnx + 4lnx = 7lnx 2lnx = 5ln + 7lnx Solving 2lnx = 5ln + 7lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. -5ln + 2lnx = 5ln + -5ln + 7lnx Combine like terms: 5ln + -5ln = 0 -5ln + 2lnx = 0 + 7lnx -5ln + 2lnx = 7lnx Add '-7lnx' to each side of the equation. -5ln + 2lnx + -7lnx = 7lnx + -7lnx Combine like terms: 2lnx + -7lnx = -5lnx -5ln + -5lnx = 7lnx + -7lnx Combine like terms: 7lnx + -7lnx = 0 -5ln + -5lnx = 0 Factor out the Greatest Common Factor (GCF), '-5ln'. -5ln(1 + x) = 0 Ignore the factor -5.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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