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