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Simplifying ln(3x) + ln(4) = ln(5 + 6x) Remove parenthesis around (3x) ln * 3x + ln(4) = ln(5 + 6x) Reorder the terms for easier multiplication: 3ln * x + ln(4) = ln(5 + 6x) Multiply ln * x 3lnx + ln(4) = ln(5 + 6x) Reorder the terms for easier multiplication: 3lnx + 4ln = ln(5 + 6x) Reorder the terms: 4ln + 3lnx = ln(5 + 6x) 4ln + 3lnx = (5 * ln + 6x * ln) 4ln + 3lnx = (5ln + 6lnx) Solving 4ln + 3lnx = 5ln + 6lnx 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. 4ln + -5ln + 3lnx = 5ln + -5ln + 6lnx Combine like terms: 4ln + -5ln = -1ln -1ln + 3lnx = 5ln + -5ln + 6lnx Combine like terms: 5ln + -5ln = 0 -1ln + 3lnx = 0 + 6lnx -1ln + 3lnx = 6lnx Add '-6lnx' to each side of the equation. -1ln + 3lnx + -6lnx = 6lnx + -6lnx Combine like terms: 3lnx + -6lnx = -3lnx -1ln + -3lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -1ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(1 + 3x) = 0 Ignore the factor -1.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 + 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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