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Simplifying ln(4x) + 2ln(x) = ln(3x) + ln(1) Remove parenthesis around (4x) ln * 4x + 2ln(x) = ln(3x) + ln(1) Reorder the terms for easier multiplication: 4ln * x + 2ln(x) = ln(3x) + ln(1) Multiply ln * x 4lnx + 2ln(x) = ln(3x) + ln(1) Multiply ln * x 4lnx + 2lnx = ln(3x) + ln(1) Combine like terms: 4lnx + 2lnx = 6lnx 6lnx = ln(3x) + ln(1) Remove parenthesis around (3x) 6lnx = ln * 3x + ln(1) Reorder the terms for easier multiplication: 6lnx = 3ln * x + ln(1) Multiply ln * x 6lnx = 3lnx + ln(1) Reorder the terms for easier multiplication: 6lnx = 3lnx + 1ln Reorder the terms: 6lnx = 1ln + 3lnx Solving 6lnx = 1ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. -1ln + 6lnx = 1ln + -1ln + 3lnx Combine like terms: 1ln + -1ln = 0 -1ln + 6lnx = 0 + 3lnx -1ln + 6lnx = 3lnx Add '-3lnx' to each side of the equation. -1ln + 6lnx + -3lnx = 3lnx + -3lnx Combine like terms: 6lnx + -3lnx = 3lnx -1ln + 3lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -1ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-1 + 3x) = 0Subproblem 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 + 3x)' equal to zero and attempt to solve: Simplifying -1 + 3x = 0 Solving -1 + 3x = 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 + 3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3x = 0 + 1 3x = 0 + 1 Combine like terms: 0 + 1 = 1 3x = 1 Add '-3x' to each side of the equation. 3x + -3x = 1 + -3x Combine like terms: 3x + -3x = 0 0 = 1 + -3x Simplifying 0 = 1 + -3x 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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