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Simplifying ln(5x + 6) = ln(x + 4) + ln(3) Reorder the terms: ln(6 + 5x) = ln(x + 4) + ln(3) (6 * ln + 5x * ln) = ln(x + 4) + ln(3) (6ln + 5lnx) = ln(x + 4) + ln(3) Reorder the terms: 6ln + 5lnx = ln(4 + x) + ln(3) 6ln + 5lnx = (4 * ln + x * ln) + ln(3) 6ln + 5lnx = (4ln + lnx) + ln(3) Reorder the terms for easier multiplication: 6ln + 5lnx = 4ln + lnx + 3ln Reorder the terms: 6ln + 5lnx = 4ln + 3ln + lnx Combine like terms: 4ln + 3ln = 7ln 6ln + 5lnx = 7ln + lnx Solving 6ln + 5lnx = 7ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7ln' to each side of the equation. 6ln + -7ln + 5lnx = 7ln + -7ln + lnx Combine like terms: 6ln + -7ln = -1ln -1ln + 5lnx = 7ln + -7ln + lnx Combine like terms: 7ln + -7ln = 0 -1ln + 5lnx = 0 + lnx -1ln + 5lnx = lnx Add '-1lnx' to each side of the equation. -1ln + 5lnx + -1lnx = lnx + -1lnx Combine like terms: 5lnx + -1lnx = 4lnx -1ln + 4lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -1ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-1 + 4x) = 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 + 4x)' equal to zero and attempt to solve: Simplifying -1 + 4x = 0 Solving -1 + 4x = 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 + 4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4x = 0 + 1 4x = 0 + 1 Combine like terms: 0 + 1 = 1 4x = 1 Add '-4x' to each side of the equation. 4x + -4x = 1 + -4x Combine like terms: 4x + -4x = 0 0 = 1 + -4x Simplifying 0 = 1 + -4x 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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